Virtually torsion-free covers of minimax groups
Virtually torsion-free covers of minimax groups
We prove that every finitely generated, virtually solvable minimax group can be expressed as a homomorphic image of a virtually torsion-free, virtually solvable minimax group. This result enables us to generalize a theorem of Ch. Pittet and L. Saloff-Coste about random walks on finitely generated, virtually solvable minimax groups. Moreover, the paper identifies properties, such as the derived length and the nilpotency class of the Fitting subgroup, that are preserved in the covering process. Finally, we determine exactly which infinitely generated, virtually solvable minimax groups also possess this type of cover.
virtually solvable group of finite rank, virtually solvable minimax group, random walks on groups
125-171
Kropholler, Peter
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Lorensen, Karl
6ae8e74b-616c-40be-8002-9c0fdcbd8c2c
April 2020
Kropholler, Peter
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Lorensen, Karl
6ae8e74b-616c-40be-8002-9c0fdcbd8c2c
Kropholler, Peter and Lorensen, Karl
(2020)
Virtually torsion-free covers of minimax groups.
Annales Scientifiques de l'Ecole Normale Supérieure, 53 (1), .
(doi:10.24033/asens.2419).
Abstract
We prove that every finitely generated, virtually solvable minimax group can be expressed as a homomorphic image of a virtually torsion-free, virtually solvable minimax group. This result enables us to generalize a theorem of Ch. Pittet and L. Saloff-Coste about random walks on finitely generated, virtually solvable minimax groups. Moreover, the paper identifies properties, such as the derived length and the nilpotency class of the Fitting subgroup, that are preserved in the covering process. Finally, we determine exactly which infinitely generated, virtually solvable minimax groups also possess this type of cover.
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Accepted/In Press date: 23 April 2018
Published date: April 2020
Keywords:
virtually solvable group of finite rank, virtually solvable minimax group, random walks on groups
Identifiers
Local EPrints ID: 420457
URI: http://eprints.soton.ac.uk/id/eprint/420457
ISSN: 0012-9593
PURE UUID: b2e65fea-14c5-4ad3-877b-c4edce8f3db4
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Date deposited: 08 May 2018 16:30
Last modified: 16 Mar 2024 06:34
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Author:
Karl Lorensen
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