Double coset decompositions of groups
Double coset decompositions of groups
We show that residually finite or word hyperbolic groups which can be decomposed as a finite union of double cosets of a cyclic subgroup are necessarily virtually cyclic, and apply this result to the study of Frobenius permutation groups. We show that in general finite double coset decompositions of a group can be interpreted as an obstruction to splitting a group as a free product with amalgamation or an HNN extension.
Frobenius groups, double coset decompositions, Bass–Serre theory, residually finite groups, word hyperbolic groups
512-518
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
1999
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Abstract
We show that residually finite or word hyperbolic groups which can be decomposed as a finite union of double cosets of a cyclic subgroup are necessarily virtually cyclic, and apply this result to the study of Frobenius permutation groups. We show that in general finite double coset decompositions of a group can be interpreted as an obstruction to splitting a group as a free product with amalgamation or an HNN extension.
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Published date: 1999
Keywords:
Frobenius groups, double coset decompositions, Bass–Serre theory, residually finite groups, word hyperbolic groups
Identifiers
Local EPrints ID: 29815
URI: http://eprints.soton.ac.uk/id/eprint/29815
ISSN: 0021-8693
PURE UUID: f389eee9-acbe-4ab6-afdc-eaaf6aa409dd
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Date deposited: 28 Jul 2006
Last modified: 16 Mar 2024 02:44
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