English

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