On the residual and profinite closures of commensurated subgroups
2019 ◽
Vol 169
(2)
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pp. 411-432
Keyword(s):
AbstractThe 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.
2011 ◽
Vol 03
(02)
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pp. 153-160
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2013 ◽
Vol 155
(3)
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pp. 379-389
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Keyword(s):
1989 ◽
Vol 106
(3)
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pp. 385-388
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2000 ◽
Vol 10
(06)
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pp. 773-782
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2019 ◽
Vol 62
(3)
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pp. 895-911
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Keyword(s):
1977 ◽
Vol 24
(1)
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pp. 117-120
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2017 ◽
Vol 39
(8)
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pp. 2248-2304
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