Chemical element of an element to exist in one of many structural forms is known as 'allotropy'. The standard state, also known as the reference state, of an element is defined as its thermodynamically most stable state at a pressure of 1 bar and a given temperature (typically at 298.15 K). In thermochemistry, an element is defined to have an enthalpy of formation of zero in its standard state. For example, the reference state for carbon is graphite, because the structure of graphite is more stable than that of the other allotropes. Several kinds of descriptive categorizations can be applied broadly to
Pure subgroup Pure subgroup In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas. A subgroup formula_1 of a (typically abelian) group formula_2 is said to be pure if whenever an element of formula_1 has an formula_4 root in formula_2, it necessarily has an formula_4 root in formula_1. Formally, formula_8 is solvable in formula_2 formula_10 is solvable in formula_1. Pure subgroups are also called isolated subgroups or serving subgroups and were first investigated in Prüfer's 1923 paper