An automorphisms $\gamma$ of a group is inertial if $X\cap X^\g$ has finite index in both $X$ and $X^\g$ 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.

### Inertial automorphisms of an abelian group

#### Abstract

An automorphisms $\gamma$ of a group is inertial if $X\cap X^\g$ has finite index in both $X$ and $X^\g$ 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/18145