The non-Abelian tensor square of a free product of groups
type: Item
instance of: scholarly article
title: The non-Abelian tensor square of a free product of groups
zbMATH Open document ID: 0635.20012
DOI: 10.1007/BF01189628
author: N. D. Gilbert
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20K45
zbMATH DE Number: 4033991
zbMATH Keywords: van Kampen theorem
zbMATH Keywords: Eilenberg-Mac Lane spaces
zbMATH Keywords: non-abelian tensor product
zbMATH Keywords: conjugation action
zbMATH Keywords: tensor square
zbMATH Keywords: free product of abelian groups
zbMATH Keywords: commutator maps
reviewed by: Jan Kubarski
MaRDI profile type: Publication
cites work: Group extensions, representations, and the Schur multiplicator
cites work: Some computations of non-Abelian tensor products of groups
cites work: Q3692477
cites work: Van Kampen theorems for diagrams of spaces
cites work: The Second Homology Group of a Group; Relations among Commutators
cites work: A certain exact sequence
full work available at URL: https://doi.org/10.1007/bf01189628
OpenAlex ID: W2083928843
description: scientific article; zbMATH DE number 4033991