Just Non-(abelian by P-type) Groups

Abstract

A group K is of P-type provided it is isomorphic to a subgroup of a finitely iterated wreath product of copies of P. For any group P, define a rooted regular tree T(P) on which P acts permuting regularly the vertices of the first level. Given a generating set A of P, we define for each element of A an automorphism of T(P) in a manner similar to the procedure in the Magnus embedding of groups. These automorphisms generate G(P, A), an extension of P. For fairly general groups P, we prove that G(P, A) is a weakly branch group whose proper quotients are abelian by P-type.