{"paper":{"title":"The group of inertial automorphisms of an abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Silvana Rinauro, Ulderico Dardano","submitted_at":"2014-03-17T18:07:19Z","abstract_excerpt":"We study the group $IAut(A)$ generated by the inertial automorphisms of an abelian group $A$, that is, automorphisms $\\gamma$ with the property that each subgroup $H$ of $A$ has finite index in the subgroup generated by $H$ and $H\\gamma$. Clearly, $IAut(A)$ contains the group $FAut(A)$ of finitary automorphisms of $A$, which is known to be locally finite. In a previous paper, we showed that $IAut(A)$ is (locally finite)-by-abelian. In this paper, we show that $IAut(A)$ is also metabelian-by-(locally finite). In particular, $IAut(A)$ has a normal subgroup $\\Gamma$ such that $IAut(A)/\\Gamma$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4193","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}