The essentially chief series of a compactly generated locally compact group
Group Theory
2017-09-19 v5
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.
Keywords
Cite
@article{arxiv.1509.06593,
title = {The essentially chief series of a compactly generated locally compact group},
author = {Colin D. Reid and Phillip R. Wesolek},
journal= {arXiv preprint arXiv:1509.06593},
year = {2017}
}
Comments
Final version; to appear in Mathematische Annalen