The essentially chief series of a compactly generated locally compact group

TL;DR

This paper establishes finiteness properties for closed normal subgroups of compactly generated locally compact groups and proves the existence of an essentially chief series with a Jordan-Hölder theorem for large factors.

Contribution

It introduces the concept of an essentially chief series for such groups and proves a Jordan-Hölder theorem for the large factors, advancing structural understanding.

Findings

Finiteness properties for closed normal subgroups

Existence of an essentially chief series

Jordan-Hölder theorem for large factors

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-H\"{o}lder theorem holds for the `large' factors in an essentially chief series.