On the nilpotency class and solvability length of nonabelian tensor products of groups

Non-abelian tensor products of solvable groups

“…Results similar to those in Corollary 2.6 have also been obtained by M. Visscher in [18]. The Corollary, for G H, already appears in [2].…”

The Non-Abelian Tensor Product of Finite Groups Is Finite: A Homology-Free Proof

“…Since w p α has p-power order, g ⊗ h has p power order for all g ∈ G, h ∈ H. By Theorem 3.4(i) of [10], G ⊗ H is a nilpotent group and hence a direct product of its Sylow subgroups.…”

“…In [10], the derivative of one group by another was introduced and its properties were investigated. DEFINITION 2.2.…”

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

“…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.…”