The essentially chief series of a compactly generated locally compact group

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 either compact, discrete, or a topological chief factor. A Jordan–Holder theorem additionally holds for the ‘large’ factors in an essentially chief series.