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

Title: A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups
Creator: Reid, Colin D.
Relation: Journal of Group Theory Vol. 24, Issue 3, p. 509-531
Publisher Link: http://dx.doi.org/10.1515/jgth-2020-0107
Publisher: Walter de Gruyter GmbH
Resource Type: journal article
Date: 2021
Description: We 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 or its dual for some n ∈ 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.
Subject: classification; abelian; isomorphism types; compact groups
Identifier: http://hdl.handle.net/1959.13/1444882
Identifier: uon:42436
Identifier: ISSN:1433-5883
Language: eng
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