Nerve net Nerve net A nerve net consists of interconnected neurons lacking a brain or any form of cephalization. While organisms with bilateral body symmetry are normally associated with a central nervous system, organisms with radial symmetry are associated with nerve nets. Nerve nets can be found in members of the Cnidaria, Ctenophora, and Echinodermata phyla, all of which are found in marine environments. Nerve nets can provide animals with the ability to sense objects through the use of the sensory neurons within the nerve net. The nerve net is the simplest form of a nervous system found in multicellular organisms. Unlike
Three subgroups lemma for all formula_13 and formula_11. Since these elements generate formula_20, we conclude that formula_21 and hence formula_4. [[Category:Theorems in group theory]] [[Category:Articles containing proofs]] [[Category:Lemmas]] 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