Inertial Automorphisms of an Abelian Group

Abstract

An automorphisms $\gamma$ of a group is inertial if $X\cap X^\gamma$ has finite index in both$X$ and $X^\gamma$ for any subgroup $X$. We study inertial automorphisms ofabelian groups and give characterization of them. In particular,if the group is periodic they have property that$X^{\langle\gamma\rangle}/X_{\langle\gamma\rangle}$ is bounded. We also study finitelygenerated groups of inertial automorphisms.