The free product of groups with amalgamated subgroup malnormal in a single factor
type: Item
instance of: scholarly article
title: The free product of groups with amalgamated subgroup malnormal in a single factor
zbMATH Open document ID: 0931.20022
DOI: 10.1016/S0022-4049(97)00157-6
author: Steven A. Bleiler
author: Amelia C. Jones
published in: Journal of Pure and Applied Algebra
publication date: 1999-08-16T00:00:00Z
review text: A proper subgroup \(S\) of \(A\) is said to be malnormal in \(A\) if the intersection of the subgroups \(aSa^{-1}\) and \(S\) is trivial if and only if \(a\) is an element of \(A\) outside of \(S\). The authors discuss groups that are free products with amalgamation, where the amalgamating subgroup is of rank at least two and malnormal in at least one of the factor groups. When the amalgamating subgroup is malnormal in a single factor and the global group is of rank two, the authors show that either the non-malnormal factor contains a torsion element or, if not, then there is a generating pair of one of four specific types. For each type, the authors establish a set of relations which must hold in the factor \(B\) and give restrictions on the rank of generators of each factor.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 1308157
zbMATH Keywords: malnormal subgroups
zbMATH Keywords: free products with amalgamation
zbMATH Keywords: generating pairs
zbMATH Keywords: relations
zbMATH Keywords: generators
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308157