2014/03/17 by Ulderico Dardano, Dardano, Ulderico, Silvana Rinauro +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1403.4193
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openalex publication_date 2014/03/17 · arxiv created 2015/05/25 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the group IAut(A) generated by the inertial automorphisms of an abelian group A, that is, automorphisms γ with the property that each subgroup H of A has finite index in the subgroup generated by H and Hγ. 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 Γ such that IAut(A)/Γ is locally finite and Γ' is an abelian periodic subgroup whose all subgroups are normal in Γ. In the case when A is periodic, IAut(A) results to be abelian-by-(locally finite) indeed, while in the general case it is not even (locally nilpotent)-by-(locally finite). Moreover, we provide further details about the structure of IAut(A) in some other cases for A.