A presentation for the stabilizer of an element in a free product
type: Item
instance of: scholarly article
title: A presentation for the stabilizer of an element in a free product
zbMATH Open document ID: 0608.20020
DOI: 10.1016/0021-8693(87)90021-4
author: Donald J. Collins
author: Heiner Zieschang
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The authors consider the free product of finitely many (freely) indecomposable groups none of which is infinite cyclic. They impose certain natural assumptions on the factors and prove that under these assumptions the stabilizer in Aut G of an element of G is finitely presented. The natural assumptions are, for example, that each factor is finitely presented, the automorphism group of each factor is finitely presented, the stabilizer of a subset of a factor in the corresponding automorphism group is finitely presented. This can be considered as a generalization (modulo the exclusion of infinite cyclic factors) of a corresponding result of \textit{J. McCool} [J. Algebra 35, 205-213 (1975; Zbl 0325.20025)] for the stabilizer of an element of a free group. The techniques used for the proofs, too technical to be explained here, are based on those developed by the authors [in their papers Math. Z. 185, 487-504 (1984; Zbl 0537.20010)] and 186, 335-361 (1984; Zbl 0542.20012)].
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 3983471
zbMATH Keywords: Whitehead method
zbMATH Keywords: free product
zbMATH Keywords: indecomposable groups
zbMATH Keywords: finitely presented
zbMATH Keywords: automorphism group
zbMATH Keywords: stabilizer
zbMATH Keywords: stabilizer of an element
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90021-4
OpenAlex ID: W2063659094
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description: scientific article; zbMATH DE number 3983471