This article is cited in 2 papers

Papers published in the English version of the journal

On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups

A. R. Chekhlov^a, P. V. Danchev<sup>b

a</sup> Section of Algebra, Faculty of Mathematics and Mechanics, Tomsk State University
^b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia

Abstract: We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper fully invariant (respectively, characteristic) subgroups isomorphic, which are studied in details by the current authors in Commun. Algebra (2015) and in J. Commut. Algebra (2023). In addition, we also explore those Abelian groups having at least one proper strongly invariant subgroup isomorphic to the whole group.

Keywords: Abelian group, characteristic subgroup, fully invariant subgroup, strongly invariant subgroup.

MSC: 20К10, 20К12

Received: 28.04.2023
Revised: 31.07.2023

Language: English

 English version: Mathematical Notes, 2023, 114:5, 716–727

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