Quasiconvex subgroups of negatively curved groups
type: Item
instance of: scholarly article
title: Quasiconvex subgroups of negatively curved groups
zbMATH Open document ID: 0822.20038
DOI: 10.1016/0022-4049(94)90063-9
author: M. Mihalik
author: Williams Towle
published in: Journal of Pure and Applied Algebra
publication date: 1995-10-09T00:00:00Z
review text: The authors prove the following theorem: Let \(H\) be a negatively curved group (that is, a hyperbolic group in the sense of Gromov) and let \(A\) be an infinite quasi-convex subgroup of \(H\). Then: (1) \(A\) has finite index in the normalizer of \(A\) in \(H\). (2) If \(h\in H\) and \(hAh^{-1}\) is a subset of \(A\), then \(hAh^{-1} = A\). (3) If \(N\) is an infinite normal subgroup of \(H\) and \(N\subset A\), then \(A\) has finite index in \(H\). Special cases of this theorem were already known, and the proof uses the basic hyperbolic group techniques.
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 681809
zbMATH Keywords: finitely generated groups
zbMATH Keywords: negatively curved groups
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: quasi-convex subgroups
zbMATH Keywords: finite index subgroups
zbMATH Keywords: normalizers
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90063-9
OpenAlex ID: W1977234254
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description: scientific article; zbMATH DE number 681809