Nonabelian tensor products and nonabelian homology of groups
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)]. Using the theory of non-abelian derived functors the author defines 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. He further shows that there is a long exact sequence in non-abelian homology, which extends the sequence in low degrees of \textit{D. Guin} [J. Pure Appl. Algebra 50, No. 2, 109-137 (1988; Zbl 0653.20051)].
long exact sequences in nonabelian homology
scientific article; zbMATH DE number 933078
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