On the residual and profinite closures of commensurated subgroups

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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