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- Title
A group of generalized finitary automorphisms of an abelian group.
- Authors
Dardano, Ulderico; Rinauro, Silvana
- Abstract
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). More precisely, IAut(A) has a normal subgroup Γ such that IAut(A)/Γ is locally finite and the derived subgroup Γ' is an abelian periodic subgroup all of whose subgroups are normal in Γ. In the case when A is periodic, IAut(A) turns out 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).
- Subjects
AUTOMORPHISMS; ENDOMORPHISMS; ABELIAN groups; FREE metabelian groups; TORSION
- Publication
Journal of Group Theory, 2017, Vol 20, Issue 2, p347
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2016-0043