Non-abelian tensor products of solvable groups

Abstract

A description of the derived series and the lower central series of a non-abelian tensor product G n H is given. For a ®nite solvable group G, we obtain an upper bound for the order of G n G.

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

“…The reader may find different proofs of Lemma 2.1(i) and (ii) also in [12]. Now we may reformulate for our aims Theorem 1.1.…”

“…Details can be found in [9,12,15]. If one looks at G and H as normal subgroups of a bigger group M , then the following argument may be applied (see for instance [9, p. 23]).…”

“…Brown and others wrote two fundamental contributions [4,5] on the so-called nonabelian tensor square of a group, leaving a series of open questions which have been successively discussed in [6,7,9,10,11,12,15,16,19,20] and in other works of different authors in recent years.…”

On the non-abelian tensor square of groups of order p4 where p is an odd prime

“…Nakaoka 8 gives the conditions that can be used to compute the non-abelian tensor of a finite group.…”

Powerful actions and non-abelian tensor products of powerful p-groups

“…In order to determine when the non-abelian tensor products of powerful p-groups are again powerful, we recall here a construction introduced by Ellis and Leonard [5] and Rocco [10]; see also Nakaoka [9]. Let M and N be groups acting compatibly upon each other and let j : N !…”