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

2020/06/06 by Colin D. Reid, Reid, Colin D.
Computer Science · Mathematics · #22B05 #22D05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:22B05 #msc:22D05

paper · pdf · doi:10.48550/arxiv.2006.03925

14 pages

arxiv created 2020/06/06 · openalex publication_date 2020/06/06 · arxiv updated 2020/06/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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.

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