Phil Wesolek : The structure of periodic elements in totally disconnected, locally compact Polish groups

Posted by Jonah Gaster , part of the Graduate Student Colloquium.

At

Feb. 4, 2013, 4:15 p.m.

In

SEO 636

Abstract

In a locally compact, totally disconnected group, $G$, an element $g\in G$ is \emph{periodic} if $cl(\langle g \rangle)$ is compact. We denote the collection of all such elements $P_1(G)$. $P_1(G)$ consists of all the elements which lie in a compact, open subgroup. Moreover, these elements play an essential role in the structure of locally compact totally disconnected groups because the topology has a basis at 1 of compact open subgroups. We study the structure of $P_1(G)$ and how it interacts with global structure. In this talk we consider how global homogeneity, algebraic, or finiteness assumptions interact with the structure of $P_1(G)$ and with the compact, open subgroups which cover $P_1(G)$.