Rendiconti del Seminario Matematico della Università di Padova

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Volume 127, 2012, pp. 213–233
DOI: 10.4171/RSMUP/127-11

Published online: 2012-12-17

Inertial Automorphisms of an Abelian Group

Ulderico Dardano[1] and Silvana Rinauro[2]

(1) Università degli Studi di Napoli Federico II, Italy
(2) Università degli Studi della Basilicata, Potenza, Italy

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 $X^{\langle\gamma\rangle}/X_{\langle\gamma\rangle}$ is bounded. We also study finitely generated groups of inertial automorphisms.

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Dardano Ulderico, Rinauro Silvana: Inertial Automorphisms of an Abelian Group. Rend. Sem. Mat. Univ. Padova 127 (2012), 213-233. doi: 10.4171/RSMUP/127-11