Maotianshan Shales fossil record. Phylum Porifera (sponges; 15 species) and Priapulida (16 species) are also well represented. Other phyla represented are Brachiopoda, Chaetognatha, Cnidaria, Ctenophora, Echinodermata, Hyolitha, Nematomorpha, Phoronida, and Chordata. Possible molluscs include "Wiwaxia" and "Nectocaris". About one in eight animals are problematic forms of uncertain affinity, some of which may have been evolutionary experiments that survived for only a brief period as benthic environments rapidly changed in the Cambrian. Chengjiang is the richest source of the lobopodia, a group including many early panarthropods, with six genera represented: "Luolishania", "Paucipodia", "Cardiodictyon"," Hallucigenia" (also known from the Burgess Shale), "Microdictyon", and "Onychodictyon".
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