The non-Abelian tensor square of a free product of groups
The non-abelian tensor product \(M\otimes N\) introduced by \textit{R. Brown} and \textit{J.-L. Loday} [C. R. Acad. Sci., Paris, Sér. I 298, 353-356 (1984; Zbl 0573.55011)] is formed from any two groups M and N such that each of M and N acts on the other. By using the conjugation action of a group G on itself the tensor square \(G\otimes G\) is always defined. In the paper reviewed the author determines the tensor square of a free product of abelian groups and computes the kernel of the commutator map for a free product in terms of the kernels of the commutator maps associated to the free factors. The kernel of the commutator map is also computed via some topological interpretations.
scientific article; zbMATH DE number 4033991