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

Colin D. Reid 1
  • 1 School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, Australia
Colin D. Reid
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  • School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia
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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 nN), 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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