Relationship of non-Abelian tensor products and non-Abelian homology of groups with Whitehead's gamma functor (Q2735699)

Given groups \(G\) and \(A\), which act on themselves by conjugation and each of which acts on the other, the non-Abelian tensor product \(G\otimes A\) was introduced by \textit{R. Brown} and \textit{J.-L. Loday} [Topology 26, 311-335 (1987; Zbl 0622.55009)]. They also related their tensor product with Whitehead's gamma functor. Using the theory of non-Abelian derived functors the author defined [in J. Pure Appl. Algebra 112, No. 2, 191-205 (1996; Zbl 0867.20041)] homology groups \(H_n(G,A)\) as the left-derived functors of the non-Abelian tensor product \(G\otimes A\), which coincide with the classical homology groups if \(A\) is Abelian. In this paper the author continues his investigations of these constructions and their variations.