- Title
- On the residual and profinite closures of commensurated subgroups
- Creator
- Caprace, Pierre-Emmanuel; Kropholler, Peter H.; Reid, Colin D.; Wesolek, Phillip
- Relation
- Mathematical Proceedings of the Cambridge Philosophical Society Vol. 169, Issue 2, p. 411-432
- Publisher Link
- http://dx.doi.org/10.1017/S0305004119000264
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2020
- Description
- 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 virtually 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.
- Subject
- residual closure; profinite closure; commensurated subgroups; profinte topologies
- Identifier
- http://hdl.handle.net/1959.13/1442203
- Identifier
- uon:41626
- Identifier
- ISSN:0305-0041
- Language
- eng
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