Nemertea analyses by molecular phylogeny are confident that members of Lophotrochozoa are more closely related to each other than of non-members, the relationships between members are mostly unclear. Most protostome phyla outside the Lophotrochozoa are members of Ecdysozoa ("animals that molt"), which include Arthropoda, Nematoda and Priapulida. Most other bilaterian phyla are in the Deuterostomia, which include Echinodermata and Chordata. The Acoelomorpha, which are neither protostomes nor deuterostomes, are regarded as basal bilaterians. Nemertea Nemertea is a phylum of invertebrate animals also known as "ribbon worms" or "proboscis worms". Alternative names for the phylum have included Nemertini, Nemertinea and Rhynchocoela. Although
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