Periodic points of algebraic actions of discrete groups

Abstract

Let $\Gamma$ be a countable group. A $\Gamma$-action on a compact abelian group $X$ by continuous automorphisms of $X$ is called Noetherian if the dual of $X$ is Noetherian as a $\mathbb{Z}(\Gamma )$-module. We prove that any Noetherian action of a finitely generated virtually nilpotent group has a dense set of periodic points.

arXiv comment12 pages, no figures