The essentially chief series of a compactly generated locally compact group

Colin D. Reid, Phillip R. Wesolek

Published 2015-09-22Version 1

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-H\"older theorem holds for the `large' factors in an essentially chief series.