The essentially chief series of a compactly generated locally compact group

2015/09/22 by Colin D. Reid, Reid, Colin D., Phillip R. Wesolek +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1509.06593

Final version; to appear in Mathematische Annalen

arxiv created 2017/09/18 · arxiv updated 2017/09/19

Abstract

We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series - i.e. a finite normal series in which each factor is compact, discrete, or a topological chief factor. Additionally, a Jordan-Hölder theorem holds for the `large' factors in an essentially chief series.

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