The Burnside problem for locally compact groups

Abstract

Using topological notions of translation-like actions introduced by Schneider, we give a positive answer to a geometric version of Burnside problem for locally compact group. The main theorem states that a locally compact group is non-compact if and only if it admits a translation-like action by the group of integers $\mathbf{Z}$. We then characterize the existence of cocompact translation-like actions of $\mathbf{Z}$ or non-abelian free groups on a large class of locally compact groups, improving on Schneider's results and generalising Seward's.

9 pages

References in corpus (1)

• Translation-like actions yield regular maps