Аннотация:
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.
The scientific work of Andrey R. Chekhlov was supported by the Ministry of
Science and Higher Education of Russia (agreement no. 075-02-2023-943).
The scientific work of Peter V. Danchev was supported in part by the Bulgarian
National Science Fund under Grant KP-06 no. 32/1 of December 07, 2019 as well as
by the Junta de Andalucía, Grant FQM 264, and by the BIDEB 2221 of TÜBÍTAK.
Образец цитирования:
A. R. Chekhlov, P. V. Danchev, “On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups”, Math. Notes, 114:5 (2023), 716–727