On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups
Group Theory
2023-08-01 v1 Rings and Algebras
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.
Cite
@article{arxiv.2307.16224,
title = {On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups},
author = {Andrey R. Chekhlov and Peter V. Danchev},
journal= {arXiv preprint arXiv:2307.16224},
year = {2023}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:2301.08924