Radical subgroups of totally disconnected locally compact groups
Group Theory
2014-05-20 v3
Abstract
We observe a correspondence between collections of closed subgroups and normal subgroups in totally disconnected locally compact groups. This correspondence is applied to prove structure theorems for two classes of totally disconnected locally compact second countable groups: the class of such groups with an open solvable subgroup and the class of such groups with a pro-nilpotent compact open subgroup. As a second application, we give new proofs and generalizations of results of G. Willis and Y. Barnea, M. Ershov, and T. Weigel on totally disconnected locally compact groups which are topologically simple and compactly generated,
Keywords
Cite
@article{arxiv.1304.7522,
title = {Radical subgroups of totally disconnected locally compact groups},
author = {Phillip Wesolek},
journal= {arXiv preprint arXiv:1304.7522},
year = {2014}
}
Comments
The results of this note will be merged into two other papers