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A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups

A classification of the abelian minimal closed normal subgroups of locally compact... AbstractWe classify the locally compact second-countable (l.c.s.c.) groups 𝐴 that are abelian and topologically characteristically simple.All such groups 𝐴 occur as the monolith of some soluble l.c.s.c. group 𝐺 of derived length at most 3; with known exceptions (specifically, when 𝐴 is Qn\mathbb{Q}^{n} or its dual for some n∈Nn\in\mathbb{N}), we can take 𝐺 to be compactly generated.This amounts to a classification of the possible isomorphism types of abelian chief factors of l.c.s.c. groups, which is of particular interest for the theory of compactly generated locally compact groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Group Theory de Gruyter

A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups

Reid, Colin D.
Journal of Group Theory , Volume 24 (3): 23 – May 1, 2021
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Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1435-4446
eISSN
1435-4446
DOI
10.1515/jgth-2020-0107
Publisher site
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Abstract

AbstractWe classify the locally compact second-countable (l.c.s.c.) groups 𝐴 that are abelian and topologically characteristically simple.All such groups 𝐴 occur as the monolith of some soluble l.c.s.c. group 𝐺 of derived length at most 3; with known exceptions (specifically, when 𝐴 is Qn\mathbb{Q}^{n} or its dual for some n∈Nn\in\mathbb{N}), we can take 𝐺 to be compactly generated.This amounts to a classification of the possible isomorphism types of abelian chief factors of l.c.s.c. groups, which is of particular interest for the theory of compactly generated locally compact groups.

Journal

Journal of Group Theory – de Gruyter

Published: May 1, 2021

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