Balanoglossus in Mashail Island described it as a worm-like holothurian. The discovery of gill-slits in this animal by Kowalewsky (1865) led to creation of a special class Enteropneusta by Gegenbaur (1870). Bateson (1885) included them in Phylum Chordata. Hyman (1959), however, placed them near Echinodermata and gave Hemichordata a status of an independent phylum. This simple organism shows affinities with several diverse groups. Balanoglossus is a tuberculos or burrowing and exclusively marine animal. It is found in shallow waters between tide marks along the coast of warm and temperate oceans. Balanoglossus clavigerus is a U-shaped excavated in a sandy bottom Nemertines
Three subgroups lemma Three subgroups lemma In mathematics, more specifically group theory, the three subgroups lemma is a result concerning commutators. It is a consequence of the Philip Hall and Ernst Witt's eponymous identity. In that which follows, the following notation will be employed: Let "X", "Y" and "Z" be subgroups of a group "G", and assume Then formula_4. More generally, if formula_5, then if formula_6 and formula_7, then formula_8. Hall–Witt identity If formula_9, then Proof of the three subgroups lemma Let formula_11, formula_12, and formula_13. Then formula_14, and by the Hall–Witt identity above, it follows that formula_15 and so formula_16. Therefore, formula_17