Groups and Dynamics Seminar

Date: January 26, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Phillip Wesolek, Binghamton University

Title: Elementary amenable groups and the space of marked groups

Abstract: The space of marked groups is a compact space that parameterizes all countable groups. This space allows for tools from descriptive set theory to be applied to study group-theoretic questions. The class of elementary amenable groups is the smallest class that contains the abelian groups and the finite groups and that is closed under group extension, taking subgroups, taking quotients, and taking countable directed unions. In this talk, we first give a characterization of elementary amenable groups in terms of a chain condition. We then show the set of elementary amenable marked groups is not in the Borel sigma algebra of the space of marked groups. This gives a new proof of a theorem of Grigorchuk: There are finitely generated amenable non-elementary amenable groups.