Function and mechanism.

The enzyme functions by attacking, hydrolyzing, and breaking glycosidic bonds in peptidoglycans. The enzyme can also break glycosidic bonds in chitin, although not as effectively as true chitinases.  Lysozymes active site binds the peptidoglycan molecule in the prominent cleft between its two domains. It attacks peptidoglycans (found in the cell walls of bacteria, especially Gram-positive bacteria), its natural substrate, between "N"-acetylmuramic acid (NAM) and the fourth carbon atom of N-acetylglucosamine (NAG).  Shorter saccharides like tetrasaccharide have also shown to be viable substrates but via an intermediate with a longer chain. Chitin has also been shown to be a viable lysozyme substrate. Artificial substrates have also been developed and used in lysozyme.

Mechanism.

Phillips.

The Phillips Mechanism proposed that the enzyme's catalytic power came from both steric strain on the bound substrate and electrostatic stabilization of an oxo-carbenium intermediate. From X-ray crystallographic data, Phillips proposed the active site of the enzyme, where a hexasaccharide binds. The lysozyme distorts the fourth sugar (in the D or -1 subsite) in the hexasaccharide into a half-chair conformation. In this stressed state, the glycosidic bond is more easily broken. An ionic intermediate containing an oxo-carbenium is created as a result of the glycosidic bond breaking. Thus distortion causing the substrate molecule to adopt a strained conformation similar to that of the transition state will lower the energy barrier of the reaction.  The proposed oxo-carbonium intermediate was speculated to be electrostatically stabilized by aspartate and glutamate residues in the active site by Arieh Warshel in 1978. The electrostatic stabilization argument was based on comparison to bulk water, the reorientation of water dipoles can cancel out the stabilizing energy of charge interaction. In Warshel's model, the enzyme acts as a super-solvent, which fixes the orientation of ion pairs and provides super-solvation (very good stabilization of ion pairs), and especially lower the energy when to ions are close to each other.  The rate-determining step(RDS) in this mechanism is related to formation of the oxo-carbenium intermediate. There were some contradictory results to indicate the exact RDS. By tracing the formation of product (p-nitrophenol), it was discovered that the RDS can change over different temperatures, which was a reason for those contradictory results. At a higher temperature the RDS is formation of glycosyl enzyme intermediate and at a lower temperature the break down of that intermediate.

Koshland.

In an early debate in 1969, Dahlquist proposed a covalent mechanism for lysozyme based on kinetic isotope effect, but for a long time the ionic mechanism was more accepted. In 2001, a revised mechanism was proposed by Vocadlo via a covalent but not ionic intermediate. Evidence from ESI-MS analysis indicated a covalent intermediate. A 2-fluoro substituted substrate was used to lower the reaction rate and accumulate an intermediate for characterization. The amino acid side-chains glutamic acid 35 (Glu35) and aspartate 52 (Asp52) have been found to be critical to the activity of this enzyme. Glu35 acts as a proton donor to the glycosidic bond, cleaving the C-O bond in the substrate, whereas Asp52 acts as a nucleophile to generate a glycosyl enzyme intermediate. The Glu35 reacts with water to form hydroxyl ion, a stronger nucleophile than water, which then attacks the glycosyl enzyme intermediate, to give the product of hydrolysis and leaving the enzyme unchanged. This covalent mechanism was named after Koshland, who first proposed this type of mechanism.  More recently, quantum mechanics/ molecular mechanics (QM/MM) molecular dynamics simulations have been using the crystal of HEWL and predict the existence of a covalent intermediate. Evidence for the ESI-MS and X-ray structures indicate the existence of covalent intermediate, but primarily rely on using a less active mutant or non-native substrate. Thus, QM/MM molecular dynamics provides the unique ability to directly investigate the mechanism of wild-type HEWL and native substrate. The calculations revealed that the covalent intermediate from the Koshland mechanism is ~30 kcal/mol more stable than the ionic intermediate from the Phillips mechanism. These calculation demonstrate that the ionic intermediate is extremely energetically unfavorable and the covalent intermediates observed from experiments using less active mutant or non-native substrates provide useful insight into the mechanism of wild-type HEWL.

Inhibition.

Imidazole derivatives can form a charge-transfer complex with some residues (in or outside active center) to achieve a competitive inhibition of lysozyme. In Gram-negative bacteria, the lipopolysaccharide acts as a non-competitive inhibitior by highly-favored binding with lysozyme.

Non-enzymatic action.

Despite that the muramidase activity of lysozyme has been supposed to play the key role for its antibacterial properties, evidence of its non-enzymatic action was also reported. For example, blocking the catalytic activity of lysozyme by mutation of critical amino acid in the active site (52-Asp -> 52-Ser) does not eliminate its antimicrobial activity. The lectin-like ability of lysozyme to recognize bacterial carbohydrate antigen without lytic activity was reported for tetrasaccharide related to lipopolysaccharide of "Klebsiella pneumoniae". Also, lysozyme interacts with antibodies and T-cell receptors.

Enzyme conformation changes.

Lysozyme exhibits two conformations: an open active state and a closed inactive state. The catalytic relevance was examined with single walled carbon nanotubes (SWCN) field effect transistors (FETs), where a singular lysozyme was bound to the SWCN FET. Electronically monitoring the lysozyme showed two conformations, an open active site and a closed inactive site. In its active state lysozyme is able to processively hydrolyze its substrate, breaking on average 100 bonds at a rate of 15 per second. In order to bind a new substrate and move from the closed inactive state to the open active state requires two conformation step changes, while inactivation requires one step.

Role in disease and therapy.

Lysozyme is part of the innate immune system. Reduced lysozyme levels have been associated with bronchopulmonary dysplasia in newborns. Piglets fed with human lysozyme milk can recover from diarrheal disease caused by "E. coli" faster. The concentration of lysozyme in human milk is 1,600 to 3,000 times greater than the concentration in livestock milk. Human lysozyme is more active than hen egg white lysozyme. A transgenic line of goats (with a founder named "Artemis") were developed to produce milk with human lysozyme to protect children from diarrhea if they can't get the benefits of human breastfeeding.  Since lysozyme is a natural form of protection from Gram-positive pathogens like "Bacillus" and "Streptococcus", it plays an important role in immunology of infants in human milk feeding. Whereas the skin is a protective barrier due to its dryness and acidity, the conjunctiva (membrane covering the eye) is, instead, protected by secreted enzymes, mainly lysozyme and defensin. However, when these protective barriers fail, conjunctivitis results.  In certain cancers (especially myelomonocytic leukemia) excessive production of lysozyme by cancer cells can lead to toxic levels of lysozyme in the blood. High lysozyme blood levels can lead to kidney failure and low blood potassium, conditions that may improve or resolve with treatment of the primary malignancy.  Serum lysozyme is much less specific for diagnosis of sarcoidosis than serum angiotensin converting enzyme; however, since it is more sensitive, it is used as a marker of sarcoidosis disease activity and is suitable for disease monitoring in proven cases.

Chemical synthesis.

The first chemical synthesis of a lysozyme protein was attempted by Prof. George W. Kenner and his group at the University of Liverpool in England. This was finally achieved in 2007 by Thomas Durek in Steve Kent's lab at the University of Chicago who made a synthetic functional lysozyme molecule.

Other applications.

Lysozyme crystals have been used to grow other functional materials for catalysis and biomedical applications. Lysozyme is a commonly used enzyme for lysing gram positive bacteria. Due to the unique function of lysozyme in which it can digest the cell wall and causes osmotic shock (burst the cell by suddenly changing solute concentration around the cell and thus the osmotic pressure), lysozyme is commonly used in lab setting to release proteins from bacterium periplasm while the inner membrane remains sealed as vesicles called the spheroplast.  For example, "E. coli" can be lysed using lysozyme to free the contents of the periplasmic space. It is especially useful in lab setting for trying to collect the contents of the periplasm. Lysozyme treatment is optimal at particular temperatures, pH ranges, and salt concentrations. Lysozyme activity increases with increasing temperatures, up to 60 degrees Celsius, with a pH range of 6.0-7.0. The salts present also affect lysozyme treatment, where some assert inhibitory effects, and others promote lysis via lysozyme treatment. Sodium chloride induces lysis, but at high concentrations, it is an active inhibitor of lysis. Similar observations have been seen with the use of potassium salts. Slight variations are present due to differences in bacterial strains.

History.

The antibacterial property of hen egg white, due to the lysozyme it contains, was first observed by Laschtschenko in 1909. The bacteria-killing activity of nasal mucous was demonstrated in 1922 by Alexander Fleming, the discoverer of penicillin, who coined the term lysozyme. Fleming reported, saying. "As this substance has properties akin to those of ferments I have called it a 'Lysozyme'." Fleming went on to show that an enzymic substance was present in a wide variety of secretions and was capable of rapidly lysing (i.e. dissolving) different bacteria, particularly a yellow "coccus" that he studied".  Lysozyme was first crystallised by Edward Abraham in 1937, enabling the three-dimensional structure of hen egg white lysozyme to be described by David Chilton Phillips in 1965, when he obtained the first 2-ångström (200 pm) resolution model via X-ray crystallography. The structure was publicly presented at a Royal Institution lecture in 1965. Lysozyme was the second protein structure and the first enzyme structure to be solved via X-ray diffraction methods, and the first enzyme to be fully sequenced that contains all twenty common amino acids. As a result of Phillips' elucidation of the structure of lysozyme, it was also the first enzyme to have a detailed, specific mechanism suggested for its method of catalytic action. This work led Phillips to provide an explanation for how enzymes speed up a chemical reaction in terms of its physical structures. The original mechanism proposed by Phillips was more recently revised.

Lysozyme, also known as muramidase or N-acetylmuramide glycanhydrolase, is an antimicrobial enzyme produced by animals that forms part of the innate immune system. Lysozyme is a glycoside hydrolase that catalyzes the hydrolysis of 1,4-beta-linkages between N-acetylmuramic acid and N-acetyl-D-glucosamine residues in peptidoglycan, which is the major component of gram-positive bacterial cell wall. This hydrolysis in turn compromises the integrity of bacterial cell walls causing lysis of the bacteria.

Lysozym (auch Muramidase) ist ein Enzym, das β-1,4-Glycosidische Bindungen zwischen N-Acetylmuraminsäure- (NAM) und N-Acetylglucosaminresten (NAG) in Peptidoglycanen, aus Zuckerderivaten und Peptiden aufgebauten Makromolekülen, hydrolysiert. Lysozyme kommen als Teil des angeborenen Immunsystems bei Tieren vor und können außerdem in Pflanzen, Pilzen, Bakterien und bei Bakteriophagen gefunden werden. Beim Menschen führen Mutationen im "LYZ"-Gen zu einer seltenen erblichen Form der Amyloidose.


History.

The city was established in 57 BC. It was one of the administrative centres of Baekje during the Three Kingdoms Period.  In 1929, during the period of Imperial Japanese rule, a confrontation between Korean and Japanese students in the city turned into Gwangju Student Independence Movement, a regional demonstration, which culminated in one of the major nationwide uprisings against Imperial Japanese cruelty during the colonial period.  The modern industry was established in Gwangju with the construction of a railway to Seoul. Some of the industries that took hold include cotton textiles, rice mills and breweries. Construction of a designated industrial zone in 1967 encouraged growth in industry, especially in the sectors linked to the automobile industry.  In May 1980, peaceful demonstrations took place in Gwangju against Chun Doo-hwan, leader of the military coup d'état of December 12, 1979. The demonstrations were suppressed by military forces, including elite units of the Special Operations Command. The situation escalated after a violent crackdown, resulting in the Gwangju Uprising, where civilians raided armories and armed themselves. By the time the uprising was suppressed 9 days later, many hundreds of civilians and several police forces / soldiers were dead. After civilian rule was reinstated in 1987, a national cemetery was established, honouring the victims of the incident.. Now the South Korean constitution admits the Gwangju Uprising as a root of South Korean democracy.  In 1986, Gwangju separated from Jeollanam-do to become a Directly Governed City (Jikhalsi), and then became a Metropolitan City (Gwangyeoksi) in 1995.  Due to a variety of factors, including the ancient rivalry between Baekje and Silla, as well as the biased priority given to the Gyeongsang region by political leaders in the 2nd half of the 20th century, Gwangju has a long history of voting for left-leaning politicians and is the main stronghold for the liberal Democratic Party of Korea along with its predecessors, as well as the progressive Justice Party.  Gwangju held many sports events such as 2002 FIFA World Cup, 2015 Summer Universiade, 2019 World Aquatics Championships.

Administrative divisions.

Gwangju is divided into 5 districts ("Gu").

Religion.

According to the census of 2005, of the people of Gwangju 33% follow Christianity (20% Protestantism and 13% Catholicism) and 14% follow Buddhism. 53% of the population is mostly not religious or follow Muism and other indigenous religions.

Population.

The population model of Gwangju is as follows;

Education.

Chonnam National University, Gwangju Institute of Science and Technology, and Gwangju Education University are public universities in Gwangju.  Honam University, Gwangju University, Gwangshin University, Gwangju Women's University, Nambu University, Chosun University, and Honam Christian University are private universities.  Gwangju Health University is a private community college offering associate degrees in humanities and social sciences, healthcare sciences, and a bachelor's degree in nursing.  Gwangju has 593 schools, consisting of 234 kindergartens, 145 elementary schools, 84 middle schools, 65 high schools, 1 science high school, 7 junior colleges, 9 universities, 38 graduate schools, and 11 others (as of 1 May 2009) with a total of 406,669 students, or 28.5% of the total city population. The average number of students per household is 0.8.

Transportation.

The city is served by the Gwangju Subway. An extension was completed in April 2008 with another due for completion in 2012. There are two KTX (high-speed rail) stations in the city: Gwangju Station and Gwangju Songjeong Station. Gwangju Songjeong station connects to the Gwangju Subway and local bus system. Now the Songjeong station is mainly used.  Gwangju has an extensive system of public buses that traverse the city. Bus stops and buses themselves contain stop information in Korean and in English. Local buses, but not the subway or KTX, connect to the intercity Gwangju Bus Terminal known as U-Square.  Gwangju is also served by the Gwangju Airport.

International relations.

Twin towns – sister cities.

Gwangju is twinned with:

Gwangju () is the sixth-largest city in South Korea. It is a designated metropolitan city under the direct control of the central government's Home Minister. The city was also the capital of South Jeolla Province until the provincial office moved to the southern village of Namak in Muan County in 2005 because Gwangju was promoted to a metropolitan city and was independent of South Jeolla province.

Gwangju, IPA Kwaŋdʑu, ist eine Stadt in der Provinz Jeollanam-do im Südwesten von Südkorea. Gwangju ist die Hauptstadt der Provinz, ist aber politisch eine eigenständige Einheit. Sie liegt etwa 330 km südlich von Seoul. Die Stadt hat 1.416.937 Einwohner, womit es die sechstgrößte des Landes ist.


Grammar.

Unserdeutsch is typical of creole languages in that it reflects the lexicon of one language overlaid upon a substrate grammar – in this case German and Tok Pisin, respectively. Grammatically, Unserdeutsch bears many similarities to L2 varieties of German, suggesting incomplete language acquisition on the part of students in the German-speaking colony. Grammatically, Unserdeutsch morphology adheres to “average” creole characteristics, but because Unserdeutsch was never formally standardized, being used only informally as an in-group register, there is an unusually high degree of grammatical variation among speakers of Unserdeutsch, both between familial groups and individual speakers.  More recently, Australian English has also influenced the language in several ways. Certain syntactic constructions appear to have been borrowed directly from English, including an English-like passive voice construction utilizing a copula. Both of these features are generally rare in creole languages, which indicates an early, pervasive English influence that might have included conscious modeling of English sentence structure.

Sentence Structure.

Unserdeutsch word order is rigidly SVO and lacks the V2 constituent order of subordinate clauses found in Standard German. This tendency extends even to imperative sentences and yes/no questions, which demonstrates a strong substrate influence from Tok Pisin.  Furthermore, even WH-fronting is optional in Unserdeutsch, and these types of interrogatives often come at the end of a sentence, as in Tok Pisin, rather than at the beginning as in Standard German or English. However, some speakers prefer to use a German-modeled sentence pattern in which the interrogative is in head position.  The use of either construction appears variable among speakers of Unserdeutsch.

Nouns.

Unserdeutsch nouns are derived almost unanimously from the German lexicon, but noun morphology is much less synthetic than Standard German. Unserdeutsch nouns do not change to indicate grammatical gender or case, nor is there overt plural marking.

Number.

Rather than taking specific singular and plural forms, as in Standard German, Unserdeutsch nouns are pluralized almost exclusively by the pronominal marker "alle", unless plurality is already indicated by a numeral or pronoun, in which case it is omitted entirely. Thus, most nouns in Unserdeutsch are pluralized as in the following example:  There are few frequently used nouns which retain Standard German plural forms and are thus double-marked for plural. These irregular forms are retained perhaps owing to frequency of use.

Articles.

Like German but unlike its substrate language, Tok Pisin, Unserdeutsch uses definite and indefinite articles. However, unlike German, these articles are not inflected for gender or case, and in fact the Standard German articles are merged into a single article "de"; this is possibly due to influence from English. Articles are normally only used with singular nouns, with the generalized plural marker "alle" functioning as an indefinite plural article. The full Unserdeutsch article set is as follows:  Speakers of Unserdeutsch often omit articles altogether in speech.

Verbs.

Nearly all Unserdeutsch verbs are lexically derived from Standard German, but the Unserdeutsch inflectional system exhibits strong influence from English and Tok Pisin, and is considerably more isolating than Standard German. Many of the distinguishing characteristics of Standard German verbs, such as separable prefixes, second- and third-person stem change and the strong/weak distinction, are not present in Unserdeutsch.

Morphology.

Verbs are generally not inflected according to person or number. Thus, the present tense form of most Unserdeutsch verbs is identical to the Standard German infinitive, which is not conjugated. A small number of verbs take an infinitive form that is instead modeled after the German third-person singular form ("geht", “go”) or verb stem ("bleib", “stay”), and some transitive verbs of English or Tok Pisin origin take the Tok Pisin suffix -"im" ("adoptim", “to adopt”). The following example illustrates verb morphology compared to Standard German:

Tense.

There is no overt preterite in Unserdeutsch, but a generalized past tense can be indicated through the use of the uninflected verb "hat" (“have”) alongside a highly regularized German participle form, which is constructed by the addition of the prefix "ge"- to the infinitive. Even verbs borrowed from English or Tok Pisin are prefixed in this way. Thus:  There are few high frequency verbs that exhibit past tense forms closer to their Standard German counterparts, although these forms are lexicalized and non-productive.  There is also a form of weakly grammaticalized future tense marked by the auxiliary "wit" (“will,” from German "wird"), which is used with the infinitive in the following way:  Overall, though, the marking of tense is optional, and many speakers of Unserdeutsch do not distinguish between tense-specific forms.

Copula.

Unusually for a creole language, Unserdeutsch has a copula which is, by contrast to the rest of the verb system, conjugated in present tense. The copular forms are very similar to their Standard German counterparts. In past tense, the copula is simply "war"; it is not conjugated at all. Thus:  Some speakers preferentially use an uninflected copula, "bis", as in:  Notably, whether inflected or not, the copula is frequently deleted in spoken Unserdeutsch.

Aspect, Mood and Voice.

The Unserdeutsch aspect system is fairly complex. Typical of a creole language, most of these constructions are formed by the addition of preverbal markers.  Progressive or habitual aspect is expressed using the so-called "am"-construction, formed using the particle "am" and the infinitive verb.  Habitual past action can be marked using the auxiliary "wit" (or sometimes "wid") along with an infinitive verb, a construction that functions similarly to English past tense would phrases. The "wit" auxiliary can also express conditional aspect, although this usage is rare.  There is no true imperative in Unserdeutsch. Command statements are formed identically to declarative clauses, and unlike English or German (but similar to Tok Pisin) these constructions retain SVO word order.  It is possible in Unserdeutsch to form directional serial verbs using the so-called "komm"-construction. This compound verb construction uses the verbs "komm" and "geht", which are reanalyzed as directional markers.  Interestingly, it is also possible to form an English-like passive voice construction using the past tense copula "war", the past participle, and the preposition "bei".  This passive construction is very rare, and is a clear example of secondary abstrate influence from English.

Negation.

Verb phrases are negated by the particle "ni" (“not,” from German "nicht"), which is usually placed at the beginning of the phrase. In a few idiomatic expressions, the negator is post-verbal, more closely mirroring German negation syntax.

Pronouns.

Unserdeutsch uses a hybrid system of personal pronouns, demonstrating heavy influence from both the substrate and lexifier languages.  Two pronouns, first-person plural "wi" and third-person singular masculine "er", have distinct object forms ("uns" and "ihm", respectively), reflecting Standard German pronominal case marking. It has been suggested by Volker (1982) that, when used in subject position, the first-person plural "uns" is exclusive, although this is disputed. Volker (1982) also identifies an object form of first-person singular, "mi", which is not attested elsewhere.

Usage.

Use of the second-person plural "eu" is rare, and "du" is sometimes substituted. The third-person pronouns mark biological sex only, and there is no equivalent to the German or English neuter forms. There are no formal pronouns in Unserdeutsch, perhaps reflecting non-European cultural conceptions of friendship and acquaintance in the South Pacific. The second-person singular "du" can be used in place of the Standard German impersonal pronoun "man", mirroring English usage. Reflexive and reciprocal pronouns are not used in Unserdeutsch; rarely, these are formed by combining the pronoun with "selbs" (“self”) or direct borrowing of the English “each other.” In some cases, personal pronouns can be omitted entirely.

Possessive Pronouns.

The Unserdeutsch possessive pronouns, while outwardly similar to their Standard German counterparts, do not take case, gender or number endings.  There is no first-person (outside of the name "Unserdeutsch") or third-person plural possessive pronoun; in order to express these forms of possession, speakers generally use a prepositional construction with "fi".

Adjectives.

With very few exceptions, Unserdeutsch adjectives are lexically identical to their German counterparts. As with other parts of speech, these adjectives are considerably more analytical than those of Standard German. Adjectives precede the referent, and show no agreement for case or gender. There is an attributive marker reanalyzed from the Standard German adjective endings into a uniform and invariant -"e", which is suffixed to an adjective that precedes a verb. Thus:  A handful of high frequency adjectives, such as "gut", retain their Standard German suppletive forms (such as "besser" and "beste").

Comparison.

The comparative forms of most Unserdeutsch adjectives are marked analytically using the particle "mehr" (“more”). The superlative is formed using the suffix -"ste", but without the vowel changes that characterize this process in Standard German. Thus, the comparative and superlative constructions are formed as follows:  A few high frequency adjectives retain their German synthetic comparative and superlative forms.

Possession.

Aside from possessive pronouns, Unserdeutsch has three constructions that mark possession, each modeled after forms found in one of the dominant languages of the area, Tok Pisin, German and English.  The first of these forms uses a preposition, "fi", to express possession, similar to the Tok Pisin "bilong"-construction.  The second form simply juxtaposes the possessor immediately before the item possessed, as is found is many dialects of German.  The last form is modeled after English, wherein the possessor takes an overt -"s" genitive suffix.  This English-modeled form is less common than the other two.

Unserdeutsch ("Our German"), or Rabaul Creole German, is a German-based creole language that originated in Papua New Guinea as a lingua franca. The substrate language is assumed to be Tok Pisin (another Germanic creole now official in Papua New Guinea, based on English which is also official), while the majority of the lexicon is from German. German was the language of instruction in Catholic mission schools, which is where the language originated, and children residing in a German-run orphanage later used the language regularly outside of their classrooms. The language developed into a first language for some when these children had families of their own. Oral stories tell a version that Unserdeutsch originated by children sharing stories where they used German vocabulary with Tok Pisin grammar, this change in language is referred to as relexification.

Unserdeutsch (auch Rabaul Creole German) ist die Sprache der Minderheit der Rabaul-Kreolen und die weltweit einzige ISO-kodierte, deutsch-basierte Kreolsprache. Ursprünglich während der deutschen Kolonialzeit in Papua-Neuguinea entstanden und nach der Auswanderung der meisten Sprecher heute überwiegend (über 90 Prozent aller Sprecher) im Osten Australiens verbreitet, ist Unserdeutsch mittlerweile so gut wie ausgestorben: Die Sprache wird heute noch von etwa einhundert Menschen gesprochen. Da es aber nur alte Sprecher gibt, ist das Verschwinden von Unserdeutsch nur eine Frage der Zeit. Die australischen Unserdeutsch-Sprecher leben heute verstreut in Städten an der Ostküste, stehen aber untereinander in geschlossenen Gruppen sozialer Netzwerke im Austausch. In Papua-Neuguinea leben heute schätzungsweise weniger als zehn Unserdeutsch-Sprecher.


Definition.

An abelian group is a set, formula_1, together with an operation formula_2 that combines any two elements formula_3 and formula_4 of formula_1 to form another element of formula_6 denoted formula_7. The symbol formula_2 is a general placeholder for a concretely given operation. To qualify as an abelian group, the set and operation, formula_9, must satisfy five requirements known as the "abelian group axioms":  A group in which the group operation is not commutative is called a "non-abelian group" or "non-commutative group".

Facts.

Notation.

There are two main notational conventions for abelian groups – additive and multiplicative.  Generally, the multiplicative notation is the usual notation for groups, while the additive notation is the usual notation for modules and rings. The additive notation may also be used to emphasize that a particular group is abelian, whenever both abelian and non-abelian groups are considered, some notable exceptions being near-rings and partially ordered groups, where an operation is written additively even when non-abelian.

Multiplication table.

To verify that a finite group is abelian, a table (matrix) – known as a Cayley table – can be constructed in a similar fashion to a multiplication table. If the group is formula_35 under the the entry of this table contains the product formula_36. The group is abelian if and only if this table is symmetric about the main diagonal.  This is true since if the group is abelian, then formula_37. This implies that the formula_38 entry of the table equals the formula_39 entry, thus the table is symmetric about the main diagonal.

Examples.

In general, matrices, even invertible matrices, do not form an abelian group under multiplication because matrix multiplication is generally not commutative. However, some groups of matrices are abelian groups under matrix multiplication – one example is the group of formula_58 rotation matrices.

Historical remarks.

Camille Jordan named abelian groups after Norwegian mathematician Niels Henrik Abel, because Abel found that the commutativity of the group of a polynomial implies that the roots of the polynomial can be calculated by using radicals. See Section 6.5 of Cox (2004) for more information on the historical background.

Properties.

If formula_42 is a natural number and formula_48 is an element of an abelian group formula_47 written additively, then formula_62 can be defined as formula_63 (formula_42 summands) and formula_65. In this way, formula_47 becomes a module over the ring formula_52 of integers. In fact, the modules over formula_52 can be identified with the abelian groups.  Theorems about abelian groups (i.e. modules over the principal ideal domain formula_52) can often be generalized to theorems about modules over an arbitrary principal ideal domain. A typical example is the classification of finitely generated abelian groups which is a specialization of the structure theorem for finitely generated modules over a principal ideal domain. In the case of finitely generated abelian groups, this theorem guarantees that an abelian group splits as a direct sum of a torsion group and a free abelian group. The former may be written as a direct sum of finitely many groups of the form formula_70 for formula_71 prime, and the latter is a direct sum of finitely many copies of formula_52.  If formula_73 are two group homomorphisms between abelian groups, then their sum formula_74, defined by formula_75, is again a homomorphism. (This is not true if formula_76 is a non-abelian group.) The set formula_77 of all group homomorphisms from formula_47 to formula_76 thus turns into an abelian group in its own right.  Somewhat akin to the dimension of vector spaces, every abelian group has a "rank". It is defined as the maximal cardinality of a set of linearly independent elements of the group. The integers and the rational numbers have rank one, as well as every subgroup of the rationals.  The center formula_80 of a group formula_47 is the set of elements that commute with every element of formula_47. A group formula_47 is abelian if and only if it is equal to its center formula_80. The center of a group formula_47 is always a characteristic abelian subgroup of formula_47. If the quotient group formula_87 of a group by its center is cyclic then formula_47 is abelian.

Finite abelian groups.

Cyclic groups of integers modulo formula_42, formula_90, were among the first examples of groups. It turns out that an arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants. The automorphism group of a finite abelian group can be described directly in terms of these invariants. The theory had been first developed in the 1879 paper of Georg Frobenius and Ludwig Stickelberger and later was both simplified and generalized to finitely generated modules over a principal ideal domain, forming an important chapter of linear algebra.  Any group of prime order is isomorphic to a cyclic group and therefore abelian. Any group whose order is a square of a prime number is also abelian. In fact, for every prime number formula_71 there are (up to isomorphism) exactly two groups of order formula_92, namely formula_93 and formula_94.

Classification.

The fundamental theorem of finite abelian groups states that every finite abelian group formula_47 can be expressed as the direct sum of cyclic subgroups of prime-power order; it is also known as the basis theorem for finite abelian groups. This is generalized by the fundamental theorem of finitely generated abelian groups, with finite groups being the special case when "G" has zero rank; this in turn admits numerous further generalizations.  The classification was proven by Leopold Kronecker in 1870, though it was not stated in modern group-theoretic terms until later, and was preceded by a similar classification of quadratic forms by Carl Friedrich Gauss in 1801; see history for details.  The cyclic group formula_96 of order formula_97 is isomorphic to the direct sum of formula_98 and formula_99 if and only if formula_45 and formula_42 are coprime. It follows that any finite abelian group formula_47 is isomorphic to a direct sum of the form  in either of the following canonical ways:  For example, formula_109 can be expressed as the direct sum of two cyclic subgroups of order 3 and 5: formula_110. The same can be said for any abelian group of order 15, leading to the remarkable conclusion that all abelian groups of order 15 are isomorphic.  For another example, every abelian group of order 8 is isomorphic to either formula_111 (the integers 0 to 7 under addition modulo 8), formula_112 (the odd integers 1 to 15 under multiplication modulo 16), or formula_113.  See also list of small groups for finite abelian groups of order 30 or less.

Automorphisms.

One can apply the fundamental theorem to count (and sometimes determine) the automorphisms of a given finite abelian group formula_47. To do this, one uses the fact that if formula_47 splits as a direct sum formula_116 of subgroups of coprime order, then formula_117.  Given this, the fundamental theorem shows that to compute the automorphism group of formula_47 it suffices to compute the automorphism groups of the Sylow formula_71-subgroups separately (that is, all direct sums of cyclic subgroups, each with order a power of formula_71). Fix a prime formula_71 and suppose the exponents formula_122 of the cyclic factors of the Sylow formula_71-subgroup are arranged in increasing order:  for some formula_125. One needs to find the automorphisms of  One special case is when formula_127, so that there is only one cyclic prime-power factor in the Sylow formula_71-subgroup formula_129. In this case the theory of automorphisms of a finite cyclic group can be used. Another special case is when formula_42 is arbitrary but formula_131 for formula_132. Here, one is considering formula_129 to be of the form  so elements of this subgroup can be viewed as comprising a vector space of dimension formula_42 over the finite field of formula_71 elements formula_137. The automorphisms of this subgroup are therefore given by the invertible linear transformations, so  where formula_139 is the appropriate general linear group. This is easily shown to have order  In the most general case, where the formula_122 and formula_42 are arbitrary, the automorphism group is more difficult to determine. It is known, however, that if one defines  and  then one has in particular formula_145, formula_146, and  One can check that this yields the orders in the previous examples as special cases (see Hillar, C., & Rhea, D.).

Finitely generated abelian groups.

An abelian group is finitely generated if it contains a finite set of elements (called "generators") formula_148 such that every element of the group is a linear combination with integer coefficients of elements of.  Let be a free abelian group with basis formula_149 There is a unique group homomorphism formula_150 such that This homomorphism is surjective, and its kernel is finitely generated (since integers form a Noetherian ring). Consider the matrix with integer entries, such that the entries of its th column are the coefficients of the th generator of the kernel. Then, the abelian group is isomorphic to the cokernel of linear map defined by. Conversely every integer matrix defines a finitely generated abelian group.  It follows that the study of finitely generated abelian groups is totally equivalent with the study of integer matrices. In particular, changing the generating set of is equivalent with multiplying on the left by a unimodular matrix (that is, an invertible integer matrix whose inverse is also an integer matrix). Changing the generating set of the kernel of is equivalent with multiplying on the right by an unimodular matrix.  The Smith normal form of is a matrix where and are unimodular, and is a matrix such that all non-diagonal entries are zero, the non-zero diagonal entries are the first ones, and is a divisor of for. The existence and the shape of the Smith normal proves that the finitely generated abelian group is the direct sum where is the number of zero rows at the bottom of (and also the rank of the group). This is the fundamental theorem of finitely generated abelian groups.  The existence of algorithms for Smith normal form shows that the fundamental theorem of finitely generated abelian groups is not only a theorem of abstract existence, but provides a way for computing expression of finitely generated abelian groups as direct sums.

Infinite abelian groups.

The simplest infinite abelian group is the infinite cyclic group formula_52. Any finitely generated abelian group formula_1 is isomorphic to the direct sum of formula_156 copies of formula_52 and a finite abelian group, which in turn is decomposable into a direct sum of finitely many cyclic groups of prime power orders. Even though the decomposition is not unique, the number formula_156, called the rank of formula_1, and the prime powers giving the orders of finite cyclic summands are uniquely determined.  By contrast, classification of general infinitely generated abelian groups is far from complete. Divisible groups, i.e. abelian groups formula_1 in which the equation formula_161 admits a solution formula_162 for any natural number formula_42 and element formula_3 of formula_1, constitute one important class of infinite abelian groups that can be completely characterized. Every divisible group is isomorphic to a direct sum, with summands isomorphic to formula_166 and Prüfer groups formula_167 for various prime numbers formula_71, and the cardinality of the set of summands of each type is uniquely determined. Moreover, if a divisible group formula_1 is a subgroup of an abelian group formula_47 then formula_1 admits a direct complement: a subgroup formula_172 of formula_47 such that formula_174. Thus divisible groups are injective modules in the category of abelian groups, and conversely, every injective abelian group is divisible (Baer's criterion). An abelian group without non-zero divisible subgroups is called reduced.  Two important special classes of infinite abelian groups with diametrically opposite properties are "torsion groups" and "torsion-free groups", exemplified by the groups formula_175 (periodic) and formula_166 (torsion-free).

Torsion groups.

An abelian group is called periodic or torsion, if every element has finite order. A direct sum of finite cyclic groups is periodic. Although the converse statement is not true in general, some special cases are known. The first and second Prüfer theorems state that if formula_1 is a periodic group, and it either has a bounded exponent, i.e., formula_178 for some natural number formula_42, or is countable and the formula_71-heights of the elements of formula_1 are finite for each formula_71, then formula_1 is isomorphic to a direct sum of finite cyclic groups. The cardinality of the set of direct summands isomorphic to formula_184 in such a decomposition is an invariant of formula_1. These theorems were later subsumed in the Kulikov criterion. In a different direction, Helmut Ulm found an extension of the second Prüfer theorem to countable abelian formula_71-groups with elements of infinite height: those groups are completely classified by means of their Ulm invariants.

Torsion-free and mixed groups.

An abelian group is called torsion-free if every non-zero element has infinite order. Several classes of torsion-free abelian groups have been studied extensively:  An abelian group that is neither periodic nor torsion-free is called mixed. If formula_1 is an abelian group and formula_190 is its torsion subgroup, then the factor group formula_191 is torsion-free. However, in general the torsion subgroup is not a direct summand of formula_1, so formula_1 is "not" isomorphic to formula_194. Thus the theory of mixed groups involves more than simply combining the results about periodic and torsion-free groups. The additive group formula_52 of integers is torsion-free formula_52-module.

Invariants and classification.

One of the most basic invariants of an infinite abelian group formula_1 is its rank: the cardinality of the maximal linearly independent subset of formula_1. Abelian groups of rank 0 are precisely the periodic groups, while torsion-free abelian groups of rank 1 are necessarily subgroups of formula_166 and can be completely described. More generally, a torsion-free abelian group of finite rank formula_156 is a subgroup of formula_201. On the other hand, the group of formula_71-adic integers formula_203 is a torsion-free abelian group of infinite formula_52-rank and the groups formula_205 with different formula_42 are non-isomorphic, so this invariant does not even fully capture properties of some familiar groups.  The classification theorems for finitely generated, divisible, countable periodic, and rank 1 torsion-free abelian groups explained above were all obtained before 1950 and form a foundation of the classification of more general infinite abelian groups. Important technical tools used in classification of infinite abelian groups are pure and basic subgroups. Introduction of various invariants of torsion-free abelian groups has been one avenue of further progress. See the books by Irving Kaplansky, László Fuchs, Phillip Griffith, and David Arnold, as well as the proceedings of the conferences on Abelian Group Theory published in "Lecture Notes in Mathematics" for more recent findings.

Additive groups of rings.

The additive group of a ring is an abelian group, but not all abelian groups are additive groups of rings (with nontrivial multiplication). Some important topics in this area of study are:

Relation to other mathematical topics.

Many large Abelian groups possess a natural topology, which turns them into topological groups.  The collection of all Abelian groups, together with the homomorphisms between them, forms the category formula_207, the prototype of an Abelian category.  There are still many areas of current research:  Moreover, Abelian groups of infinite order lead, quite surprisingly, to deep questions about the set theory commonly assumed to underlie all of mathematics. Take the Whitehead problem: are all Whitehead groups of infinite order also free Abelian groups? In the 1970s, Saharon Shelah proved that the Whitehead problem is:

A note on the typography.

Among mathematical adjectives derived from the proper name of a mathematician, the word "abelian" is rare in that it is often spelled with a lowercase a, rather than an uppercase A, indicating how ubiquitous the concept is in modern mathematics.

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.

Eine abelsche Gruppe ist eine Gruppe, für die zusätzlich das Kommutativgesetz gilt. Der mathematische Begriff abelsche Gruppe, auch kommutative Gruppe genannt, verallgemeinert das Rechnen mit Zahlen. Addition rationaler Zahlen und die Multiplikation rationaler Zahlen formula_1 erfüllen eine Reihe gemeinsamer Gesetze. Diese Regeln kommen oft in Geometrie und Algebra vor. So zum Beispiel bei Verschiebungen, Drehungen der Ebene um einen Punkt, Addition von Funktionen. Ornamente in Kunst und Natur zeichnen die Spuren abelscher Gruppen. Deswegen wird von der speziellen Bedeutung des Additionszeichens formula_2 und des Multiplikationszeichens formula_3 abstrahiert und der Begriff der kommutativen oder abelschen Gruppe geschaffen. Der Name ist zu Ehren des norwegischen Mathematikers Niels Henrik Abel gewählt worden.


History.

Triple P, or the "Positive Parenting Program", was created by Matthew R. Sanders and colleagues, in 2001. at the University of Queensland in Australia and evolved from a small “home-based, individually administered training program for parents of disruptive preschool children” into a comprehensive preventive intervention program (p. 506). This program was inspired by health promotion programs aimed at impacting people at the population level. The overall goal of the program is to enhance the knowledge, skills, and confidence of parents in order to prevent behavioral, emotional, and developmental problems in children and adolescents.

Program elements.

Overview.

There are five developmental periods that are targeted from infancy to adolescence. At each developmental period, the range of the program can be either broad and target the entire population or it can be specific and target only at-risk children. The program addresses social contexts that influence parents’ daily life: mass media, primary health care services, child care and school systems, work sites, religious organizations, and the broader political system (p. 507). The multilevel nature of the program is designed to increase efficiency, minimize costs, and ensure dissemination. The design also maximizes usage of existing community resources.

Programs.

In addition to the program for younger children (Standard Triple P), there are versions of Triple P for families with specific needs, including parents of adolescents (Teen Triple P), parents with a child with a disability (Stepping Stones Triple P) and parents who are separated or divorced (Family Transitions Triple P).)

Research.

Evidence for the effectiveness of intervention programs can be divided into two types. One type is impact studies where the aim of the evaluation is to demonstrate a statistically significant improvement in outcomes on a population, which can be attributed to the intervention. A second type is qualitative studies which aim to illuminate the mechanisms through which program participants can access the resources and help offered in the program to achieve better outcomes.  Nowak and Heinrichs (2008) conducted a meta-analysis that analyzed findings of 55 research studies on the Positive Parenting Program and found reliable positive effects of the program across all settings (initial levels of problems and countries) for child behavior problems, parenting behavior, and parental well-being. Parents’ relationship quality also significantly improved as a result of the program. The findings were unable to establish whether positive child effects were due to an increase in positive behavior or a decrease in problematic behavior. According to the authors, the results of the meta-analysis indicated the program’s “ability to effect meaningful improvements in parents and children” (p. 114). Furthermore, Triple P has also been provided to families in the United Kingdom where neglect is a concern. The findings from this service showed that, on average the children who participated in the evaluation experienced improved emotional and behavioural outcomes. However this positive change could not be attributed to Triple P because a control group had not been established.  A critical 2012 systematic review and meta-analysis of these interventions revealed many small, underpowered and poorly-controlled studies, with substantial risk of reporting bias, triggering a response from a group including many Triple-P authors. Another commentary in the same journal claimed the response did not adequately address the critique and indicated that commitments to such programmes by policy-makers needs to be based on sound evidence, or risks wasting money. A later meta-analysis by a group including Triple-P authors was published in 2014 claiming widespread benefits in the short and long term.  Qualitative research studies have also illuminated some of the ways in which programs can help individual parents. An evaluation of the Triple P intervention highlighted how many parents were able to improve the way in which they related to their children after having received advice about how to be clear and boundaries with their children, and in some cases after having tried and seen the effects of such approaches for themselves, first-hand, and often for the first time.

Triple P is a parenting intervention with the main goals of increasing the knowledge, skills, and confidence of parents and reducing the prevalence of mental health, emotional, and behavioral problems in children and adolescents. The program was originally specifically tailored for at risk children and parents, but there are now different levels of Triple P designed to work together as a broad, universal, public health approach. This program is based on principles of community psychology.

Triple P (engl. für "Dreifaches P" von "Positive Parenting Program") ist ein auf verhaltenstherapeutischer sowie klinisch-psychologischer Grundlage aufbauendes Erziehungsprogramm. Es wurde von Matt Sanders und seiner Arbeitsgruppe an der University of Queensland in den 1980er Jahren entwickelt, um Eltern bei der Erziehung ihrer Kinder zu helfen.


Inception.

As an elector for the District of the Carmes Déchaussés in 1789, Marat tried to persuade the electoral assembly to publish a journal to keep their electorate informed of current political events. When they did not take up his proposal, Marat resigned his post as elector in order to concentrate on writing a journal himself, at first entitled "Le Publiciste parisien". The first issue was published September 12, 1789. After several issues, the name was changed to "L’Ami du peuple".

Early struggles.

The journal was printed in octavo format, usually eight pages long, although occasionally expanding to twelve or sixteen pages. Marat ordinarily published "L’Ami du Peuple" on a daily basis, but there are several gaps in its publication due to Marat’s several times going into hiding to avoid arrest, during which he did not print his journal. His continual attacks against Jacques Necker, Jean Sylvain Bailly, the comte de Mirabeau, the Paris Commune, the marquis de Lafayette, the National Constituent Assembly, the Legislative Assembly, the National Convention, the émigrés, and King Louis XVI himself caused several decrees of outlawry and accusation against him and attempts to suppress his journal. His press was destroyed and copies of "L’Ami du peuple" confiscated at least twice. On one occasion his printer was arrested and imprisoned, and the plates used to print an especially controversial issue—in which he threatened to tear out the heart of Lafayette, burn the King, and impale the deputies of the Assembly upon their seats—were destroyed.  Marat, with no source of independent income, used much of his own savings to print "L’Ami du peuple". In early 1792, after returning from a two-month stay in England, he could not afford to continue the journal. With the financial support of his new common-law wife, Simonne Evrard, he was able to renew publication. After the suspension of the monarchy on August 10, 1792, the Committee of Police and Surveillance of the Paris Commune gave Marat four of the royal presses, and the new "imprimerie de Marat" was set up in the basement of the Convent of the Cordeliers.

Marat's time in National Convention.

On September 9, 1792, Marat was elected to the National Convention. On September 25, he began a new journal entitled "Journal de la République française". In April 1793, the Girondists passed a law (later repealed) making it illegal for members of the Convention to be at the same time legislators and journalists; in response, Marat changed the name of his journal again—this time to "Publiciste de la Révolution française"—claiming to be a publicist, not a journalist. It would continue under this name until his death.  Marat resigned from the Convention on June 3, 1793, after the overthrow of the Girondists was complete. His skin disease was now accompanied by a lung complaint, and he spent much of his time in a medicinal bath. His journal during this time consists mostly of letters from his many correspondents. On July 13, Marat was murdered by Charlotte Corday; the last edition of his journal was published the day after his death.

Impact and influence.

In all, Marat's "L’Ami du peuple" ran to nearly seven hundred issues, and the journal he began at his election to the Convention ran to nearly two hundred and fifty issues, in addition to his many other pamphlets. The popularity of his paper led to many counterfeits during his periods of hiding (by those in sympathy with his views and those wishing to misrepresent him) and after his death. His incendiary journalism is credited with playing a significant role in the Women's March on Versailles in October 1789, the suspension of the monarchy on August 10, 1792, the September Massacres and inciting other actions of the revolutionary crowd.

In Marat's own words.

Marat describes the start and evolution of his journal (alongside his political views) in his journal of March 19, 1793:  At the outbreak of the Revolution, wearied by the persecutions that I had experienced for so long a time at the hands of the Academy of Sciences, I eagerly embraced the occasion that presented itself of defeating my oppressors and attaining my proper position. I came to the Revolution with my ideas already formed, and I was so familiar with the principles of high politics that they had become commonplaces for me. Having had greater confidence in the mock patriots of the Constituent Assembly than they deserved, I was surprised at their pettiness, their lack of virtue. Believing that they needed light, I entered into correspondence with the most famous deputies, notably with Chapelier, Mirabeau, and Barnave. Their stubborn silence on all my letters soon proved to me that though they needed light, they cared little to be enlightened. I adopted the course of publishing my ideas by means of the press. I founded the Ami du Peuple. I began it with a severe but honest tone, that of a man who wishes to tell the truth without breaking the conventions of society. I maintained that tone for two whole months. Disappointed in finding that it did not produce the entire effect that I had expected, and indignant that the boldness of the unfaithful representatives of the people and of the lying public officials was steadily increasing, I felt that it was necessary to renounce moderation and to substitute satire and irony for simple censure. The bitterness of the satire increased with the number of mismanagements, the iniquity of their projects and the public misfortunes. Strongly convinced of the absolute perversity of the supporters of the old regime and the enemies of liberty, I felt that nothing could be obtained from them except by force. Revolted by their attempts, by their ever-recurrent plots, I realized that no end would be put to these except by exterminating the ones guilty of them. Outraged at seeing the representatives of the nation in league with its deadliest enemies and the laws serving only to tyrannize over the innocent whom they ought to have protected, I recalled to the sovereign people that since they had nothing more to expect from their representatives, it behooved them to mete out justice for themselves. This was done several times.

L'Ami du peuple (, "The Friend of the People") was a newspaper written by Jean-Paul Marat during the French Revolution. "The most celebrated radical paper of the Revolution", according to historian Jeremy D. Popkin, "L’Ami du peuple" was a vocal advocate for the rights of the lower classes against those Marat believed to be enemies of the people, which he had no hesitation mentioning in his writings. These papers were considered dangerous because they often ignited violent and rebellious behavior.

Der L'Ami du Peuple (Der Volksfreund) war eine von Jean-Paul Marat herausgegebene und verfasste Zeitung, die während der Zeit der Französischen Revolution auf Seiten des Volkes die führenden Köpfe der Gegenrevolution und deren Politik scharf angriff. Selbst nachdem revolutionäre Volksvertreter wie Robespierre die Regierung übernommen hatten, nahm das Blatt seine regierungskritische Rolle weiterhin wahr und verlangte unter anderem die Einführung der Verfassung von 1793, um somit dem Volk umfassendere Rechte zu verschaffen.


Name.

The most common Latin spellings of the Gepid name in plural used a "p", but varied concerning the vowels: Gepidae, Gipidae, Gipedae, Gipides. Similarly, Procopius writing in Greek uses a stem γηπαιδ- which should be transliterated as Giped-. All these forms are interpreted by modern linguists as Gothic-influenced. Forms from Langobard, Old Norse and Old English however indicate that the "p" was really a "b" sound, and modern linguists reconstruct the original Germanic form as *"Gíbidoz", based on the Germanic verb "to give" (as still found in English) and apparently indicating that they named themselves gifted or rewarded or generous.  The Gepids are generally equated to the people mentioned in the Old English "Widsith" and "Beowulf", as'or. These names are etymologically equivalent Old English forms of Gepidae; they could not have arisen through borrowing from attested Latin forms. Walter Goffart has objected to the identification of the Old English'and with the Gepids.

Medieval etymologies.

Jordanes in the 6th century, reported in his Gothic origins story the "Getica", that the name of the Gepids came from "gepanta", an insult in Gothic meaning "sluggish, stolid" ("pigra"), because the Gepids had lagged behind their Gothic kin when they migrated more than a thousand years earlier.  Isidore of Seville in his etymologies, interpreted the second part of the Gepid name as "feet" (Latin "pedes") and explained that the Gepids were known for going into battle on foot ("pedestri"), rather than mounted. The much later (12th century) Byzantine "Etymologicum Magnum" interprets the name using the Greek word for children, making the Gepids "Gētípaides" (Γητίπαιδες) meaning "children of the Goths (equated to Getae)". All three of these texts follow a tradition of seeing the Gepids as "offshoots or close relatives of the Goths".

Language.

There is little direct evidence for the original language of the Gepids, but they were clearly Gothic in culture during the period when the Romans reported upon them. The 6th-century Byzantine writer, Procopius, listed the Gepids among the "Gothic nations," along with the Vandals, Visigoths, and Goths proper, in his "Wars of Justinian", "sharing the same language, white bodies, blond hair, and Arian form of Christianity".

History.

Legendary.

All information of the Gepids' origins came from "malicious and convoluted Gothic legends," recorded in Jordanes' "Getica" after 550. According to Jordanes's narration the northern island of "Scandza," which is associated with Sweden by modern scholars, was the original homeland of the ancestors of the Goths and Gepids. They left Scandza together in three boats under the leadership of Berig, the legendary Gothic king. Jordanes specified that the Gepids' ancestors traveled in the last of the three ships, for which their fellows mocked them as "gepanta", or "slow and stolid." The Goths and Gepids then settled along the southern shore of the Baltic Sea on an island at the mouth of the Vistula river, called "Gepedoius," or the Gepids' fruitful meadows, by Jordanes. Modern historians debate whether the part of Jordanes's work which described the migration from Scandza was written at least partially on the basis of Gothic oral history or whether it was an "ahistorical fabrication." Jordanes's passage in his "Getica" reads:  According to Jordanes, the Gepids decided to leave "Gepedoius" during the reign of a king named Fastida. He claims the Gepids moved to the south long after the Goths had already moved, and defeated the Burgundians and other races, provoking the Goths in the process. Fastida demanded land from Ostrogotha, King of the Visigoths, because the Gepids' territory was "hemmed in by rugged mountains and dense forests". Ostrogotha refused Fastida's demand and the Gepids joined battle with the Goths "at the town of Galtis, near which the river Auha flows". They fought until darkness fell, when Fastida and his Gepids withdrew from the battlefield and returned to their land.

Before the arrival of the Huns.

The Gepids were the "most shadowy of all the major Germanic peoples of the migration period," according to historian Malcolm Todd. Neither Tacitus nor Ptolemy mentioned them in their detailed lists of the "barbarians" in the 1st and 2nd centuries AD. They first appear only in the late, and by this time they are already living in or near the area where they remained for the rest of their known history.  According to the unreliable "Augustan History" of Emperor Claudius Gothicus (VI.2), Gepids were involved in the "Scythian" invasion of the Roman provinces in the Balkan Peninsula in 269, but routed them. Others listed were Greuthungi, Ostrogoths, Tervingi, Vesi, Peucini, Heruli and Celts. The same source also says that Emperor Probus, who ruled between 276 and 282, settled Gepid, Vandals, and Greuthungi prisoners of war in the Roman Empire in the Balkans.  In the 11th panegyric to emperor Maximian given in Trier in 291, which is also the first time the Tervingi and Taifali were mentioned, the passage described a battle outside the empire where the Gepids were on the side of the Vandals, attacked by Taifali and a "part" of the Goths. The other part of the Goths had defeated the Burgundians who were supported by Tervingi and Alemanni. They were however "remote enough from the imperial frontier for them not to appear in the Verona list or in the histories of Ammianus or Orosius".  Modern historians who write of the Gepids' early history sometimes apply a "mixed argumentation", combining Jordanes' narration with results of archaeological research. Historian István Bóna says that the battle mentioned in the panegyric was about 290 in the former province of Dacia, equating it to the battle mentioned by Jordanes, involving Fastida. Archaeologist Kurdt Horedt however also equates it to the battle involving Fastida and proposed that the battle took place east of the Carpathian Mountains after 248 and before the withdrawal of the Romans from the province of Dacia in the early 270s. Walter Pohl only says that the battle must have happened between 248 and 291, and could have been inside or outside the curve of the Carpathians, though he feels it is obvious that it must in the region of the formerly Roman province of Dacia in Transylvania.  The Gepids' history in the is unknown, because no written source mentioned them during this period. The silence of the Roman sources suggests that their homeland did not border on the Roman Empire. On the basis of Jordanes' reference to the "rugged mountains" of the Gepids' land, historians locate it near the Carpathians, along the upper courses of either the Tisza or the Dniester rivers, in the late. The exact date of the Gepids' settlement in the Carpathian Basin cannot exactly be determined. Archaeologist István Bóna says they were present in the northeastern region already in the 260s. According to Coriolan H. Opreanu, they seem to have arrived around 300. Archaeologists Eszter Istvánovits and Valéria Kulcsár write that no archaeological evidence substantiates the Gepids' presence before around 350.  Graves from the which yielded swords, lances and shields with iron boss were unearthed in cemeteries between the rivers Tisza and Körös (in present-day north-eastern Hungary and north-western Romania). Many scholars (including Kurdt Horedt, István Bóna and Coriolan H. Opreanu) attribute those graves to Gepid warriors. Graves of women from the same cemeteries produced artefacts—including bronze and silver clasps, bone combs, and fibulae—which are similar to objects found in the cemeteries of the nearby "Sântana de Mureș-Chernyakhov culture". István Bóna writes that the spread of these cemeteries shows that the Gepids subjugated the Germanic Victohali, who had previously inhabited the same region, before expanding towards the Mureș River in the middle of the.

Within the Hunnic Empire.

A large group of diverse peoples from the region of the Middle Danube crossed the river Rhine and invaded the Roman Empire in 405 or 406. Although most contemporaneous sources only listed the Vandals, Alans and Sueves among the invaders, according to St. Jerome, who lived in Bethlehem around that time, Gepids also participated in the invasion. According to a scholarly theory, the westward migration of the Huns forced the tribes to flee from the Carpathian Basin and seek refuge in the Roman Empire. Whatever the exact sequence of events, the Middle Danube region was subsequently dominated by peoples from the east, associated with Goths and Huns.  Jordanes reported that Thorismund, King of the Ostrogoths, who was subjected to the Huns, "won a great victory over" the Gepids, but fell in the battle. Jordanes' report suggests that the Gepids were forced to accept the overlordship of the Ostrogoths, within the emerging Hunnic Empire. A treasure of gold jewels, which was found at Șimleu Silvaniei, was hidden in the first decades of the, most probably in connection with the struggles ending with the Gepids' subjection to the Huns, according to István Bóna.  The Gepid warriors fought on the side of the Huns during the next decades. According to Jordanes, Attila the Hun prized Ardaric, King of the Gepids, and Valamir, King of the Ostrogoths, "above all the other chieftains", who were subjected to the Huns, in the 440s, according to Jordanes. Goffart, sceptical of Jordanes, has suggested that "scattered evidence", including descriptions of Attila himself as a Gepid, suggests that Ardaric and the Gepids may have been more important than the Ostrogoths under Attila.  The Gepids' participation in the Huns' campaigns against the Roman Empire brought them much booty, contributing to the development of a rich Gepid aristocracy. Especially, the isolated graves of 5th-century aristocratic women evidence the Gepid leaders' wealth: they wore heavy silver fibulas on their shoulders, bead necklaces, silver bracelets, large gold earrings, and silver clasps on their clothes and belts. A "countless host" under the command of Ardaric formed the right wing of the army of Attila the Hun in the Battle of the Catalaunian Plains in 451. On the eve of the main encounter between allied hordes, the Gepids and Franks met each other, the latter fighting for the Romans and the former for the Huns, and seem to have fought one another to a standstill with 15,000 dead.  Attila the Hun died unexpectedly in 453. Conflicts among his sons developed into a civil war, enabling the subject peoples to rise up in rebellion. According to Jordanes, the Gepid king, Ardaric, who "became enraged because so many nations were being treated like slaves of the basest condition", was the first to take up arms against the Huns. The decisive battle was fought at the (unidentified) Nedao River in Pannonia in 454 or 455. In the battle, the united army of Gepids, Rugii, Sarmatians and Suebi routed the Huns and their allies, including the Ostrogoths. It was the Gepids who took the lead among the old allies of Attila, and establishing one of the largest and most independent new kingdoms, thus acquiring the "capital of esteem that sustained their kingdom for more than a century".

Kingdom of the Gepids.

After the Battle of Nedao, the Hunnic Empire disintegrated and the Gepids became the dominant power in the eastern regions of the Carpathian Basin. According to Jordanes, the Gepids "by their own might won for themselves the territory of the Huns and ruled as victors over the extent of all Dacia, demanding of the Roman Empire nothing more than peace and an annual gift" after their victory. Emperor Marcian confirmed their status as the allies of the empire and granted them an annual subsidy of 100 pounds of gold. The late-5th-century treasures excavated at Apahida and Someșeni show that the Gepid rulers accumulated great wealth in the second half of the century.  The Gepids joined a coalition formed by the Suebi, Scirii, Sarmatians and other peoples formed against the Ostrogoths who had settled in Pannonia. However, the Ostrogoths routed the united forces of their enemies in the Battle of Bolia in 469. After the Ostrogoths left Pannonia in 473, the Gepids captured Sirmium (now Sremska Mitrovica in Serbia), a strategically important town on the road between Italy and Constantinople.  In 489, Thraustila, King of the Gepids, tried to hinder the Ostrogoths from crossing the river Vuka during Theoderic the Great's campaign against Italy, but the Ostrogoths routed Thraustila's army. The Gepids also lost Sirmium to the Ostrogoths, according to Walter Pohl. In short, according to Walter Goffart, Thraustila's son, Thrasaric, "regained control of Sirmium but possibly under Ostrogothic underlordship". Theoderic the Great dispatched one "comes" Pitzia to launch a campaign against the Gepids who either tried to capture Sirmium or wanted to get rid of Theoderic's suzerainty in 504. Comes Pitzia expelled the Gepid troops from Sirmium without much resistance.  In an attempt to take advantage of the death of Theoderic the Great in 526, the Gepids invaded the region of Sirmium in 528 or 530, but Vitiges defeated them.  The Gepids reached the zenith of their power after 537, settling in the rich area around Singidunum (today's Belgrade). For a short time, the city of Sirmium (present-day Sremska Mitrovica) was the center of the Gepid State and the king Cunimund minted golden coins in it.  In 546 the Byzantine Empire allied themselves with the Lombards, and in 552 the Gepids suffered a disastrous defeat from Alboin, king of the Lombards, in the Battle of Asfeld, after which Alboin had a drinking cup made from the skull of Cunimund.

Fall and last records.

The Gepids were finally overrun by the Avars in the 567 Lombard-Gepid war. Many Gepids followed Alboin to Italy in 568 according to Paulus Diaconus, but many remained in the area of their old kingdom. In 630, Theophylact Simocatta reported that the Byzantine Army entered the territory of the Avars and attacked a Gepid feast, capturing 30,000 Gepids (they met no Avars).  Recent excavation by the Tisza River at Szolnok brought up a Gepid nobleman from an Avar period grave who was also wearing Turkic-Avar pieces next to the traditional Germanic clothes in which he was buried.  In the 8th century, Paul the Deacon lists Gepid, Bulgarian, Sarmatian, Pannonian, Suabian and Norican villages in Italy but we do not know if Paul means in his own day or is simply lifting the phrase from an older source.

Archeological sites.

Numerous archaeological sites have been attributed to the Gepids. The first scientific excavations of such an attributed Gepid site were done by István Kovács at Band in 1906 and 1907.  In Vlaha, Cluj County, Romania, a necropolis was discovered in August 2004 with over two hundred tombs dated to the 6th century AD. Eighty-five percent of the discovered tombs were robbed in the same period. The remaining artifacts are ceramics, bronze articles and an armory. Also in Romania, at Miercurea Sibiului, there is another necropolis with rich artifacts. Other necropolises in Romania are:  Gepid treasures were also found at Someșeni and Șimleu Silvaniei.

The Gepids () were an East Germanic tribe who lived in the area of modern Romania, Hungary and Serbia, roughly between the Tisza, Sava and Carpathian mountains. They were closely related to, or a subdivision of, the Goths.

Die Gepiden (auch "Gepidi", "Gebidi"; lateinisch "Gipedae", "Gepidae") waren ein ostgermanischer Stamm im Gebiet der heutigen Staaten Ungarn und Rumänien, der möglicherweise mit den Goten verwandt war. Sie wurden bekannt, als sie unter Ardarich in der Schlacht am Nedao (454 oder 455) die Söhne Attilas aus dem heutigen Ungarn vertrieben. Das danach errichtete Gepidenreich an der mittleren Donau bestand noch bis ins 6. Jahrhundert.


Iron gall ink.

Oak galls have been used in the production of ink since at least the time of the Roman Empire. From the Middle Ages to the early twentieth century, iron gall ink was the main medium used for writing in the Western world.  Gall nuts are a source of tannin in the production of iron gall ink. Tannins belong to a group of molecules known as polyphenols and can be taken from different parts of plants such as leaves, pods, fruits, and gall nuts.  Along with gall nuts, other important ingredients in the production of iron gall ink include iron sulfate and gum arabic. The reaction between the tannins from the gall nut and the iron produces a complex that gives the iron gall its color. The gum arabic makes the ink more viscous and helps bind the ink to the writing surface.

Folklore.

It is said that if a "worm" is found inside the gall on Michaelmas Day, then the year will be pleasant and unexceptional, and if a spider is found, then it will be a bad year with shortages and ruined crops. If a fly is found inside, then it will be a moderate season, and if nothing is found, then serious diseases will occur all that year.  Oak Apple Day (or Royal Oak Day) is a former public holiday in England on 29 May that commemorated the Restoration of Charles II in 1660. The popular name refers to the event during the English Civil War when Charles hid in an oak tree. The commemoration persists in some areas today, although festivities have little to do with the Restoration.

Oak apple or oak gall is the common name for a large, round, vaguely apple-like gall commonly found on many species of oak. Oak apples range in size from in diameter and are caused by chemicals injected by the larva of certain kinds of gall wasp in the family Cynipidae. The adult female wasp lays single eggs in developing leaf buds. The wasp larvae feed on the gall tissue resulting from their secretions, which modify the oak bud into the gall, a structure that protects the developing larvae until they undergo metamorphosis into adults.

Der rundliche Gallapfel, auch Eichengalle, Eichengallapfel und Blattgalle (von lateinisch "galla") genannt, ist eine Pflanzengalle, die im Herbst an der Unterseite von Eichenblättern, insbesondere von "Quercus infectoria", aber auch von der Traubeneiche und der Stieleiche, vorkommt. Er entsteht durch abgelegte befruchtete Eier von Gallwespen (Cynipidae), etwa der Gemeinen Eichengallwespe ("Cynips quercusfolii").