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 of abelian groups and give characterization of them. In particular, if the group is periodic they have property that $X^{⟨\gamma ⟩}/X_{⟨\gamma ⟩}$ is bounded. We also study finitely generated groups of inertial automorphisms.