Graduate Student Colloquium
Phil Wesolek
UIC
The structure of periodic elements in totally disconnected, locally compact Polish groups
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 $P_1(G)$.
Monday February 4, 2013 at 4:15 PM in SEO 636