On the residual and profinite closures of commensurated subgroups
On the residual and profinite closures of commensurated subgroups
The residual closure of a subgroup H of a group G is the intersection of all virtually normal subgroups of G containing H. We show that if G is generated by finitely many cosets of H and if H is commensurated, then the residual closure of H in G is virtu- ally normal. This implies that separable commensurated subgroups of finitely generated groups are virtually normal. A stream of applications to separable subgroups, polycyclic groups, residually finite groups, groups acting on trees, lattices in products of trees and just-infinite groups then flows from this main result.
profinite closure, reisidual finiteness
411-432
Caprace, Pierre-Emmanuel
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Kropholler, Peter H.
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Reid, Colin D.
e6ef4078-a882-4960-8c25-fd97d1679b1a
Wesolek, Phillip
726315f9-6185-4951-a47b-26d04e0f3cd8
September 2020
Caprace, Pierre-Emmanuel
a89ce108-f919-4fbd-9d6f-99b9af6abb81
Kropholler, Peter H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Reid, Colin D.
e6ef4078-a882-4960-8c25-fd97d1679b1a
Wesolek, Phillip
726315f9-6185-4951-a47b-26d04e0f3cd8
Caprace, Pierre-Emmanuel, Kropholler, Peter H., Reid, Colin D. and Wesolek, Phillip
(2020)
On the residual and profinite closures of commensurated subgroups.
Mathematical Proceedings of the Cambridge Philosophical Society, 169 (2), .
(doi:10.1017/S0305004119000264).
Abstract
The residual closure of a subgroup H of a group G is the intersection of all virtually normal subgroups of G containing H. We show that if G is generated by finitely many cosets of H and if H is commensurated, then the residual closure of H in G is virtu- ally normal. This implies that separable commensurated subgroups of finitely generated groups are virtually normal. A stream of applications to separable subgroups, polycyclic groups, residually finite groups, groups acting on trees, lattices in products of trees and just-infinite groups then flows from this main result.
Text
On the residual and profinite closures of commensurated subgroupspdf
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More information
Accepted/In Press date: 14 May 2019
e-pub ahead of print date: 30 July 2019
Published date: September 2020
Keywords:
profinite closure, reisidual finiteness
Identifiers
Local EPrints ID: 431925
URI: http://eprints.soton.ac.uk/id/eprint/431925
ISSN: 0305-0041
PURE UUID: ddc9687f-77a6-4a0f-83dc-4b18cd535eb4
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Date deposited: 21 Jun 2019 16:30
Last modified: 16 Mar 2024 07:56
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Contributors
Author:
Pierre-Emmanuel Caprace
Author:
Colin D. Reid
Author:
Phillip Wesolek
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