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Matematicheskie Zametki, 2023, Volume 114, Issue 5, paper published in the English version journal (Mi mzm14093)  
This article is cited in 1 scientific paper (total in 1 paper)

Papers published in the English version of the journal

On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups

A. R. Chekhlova , P. V. Danchevb

a Section of Algebra, Faculty of Mathematics and Mechanics, Tomsk State University
b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia
Citations (1)
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-943
Bulgarian National Science Fund 32/1
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía 264
Scientific and Technological Research Council of Turkey (TÜBITAK) 2221
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.
Received: 28.04.2023
Revised: 31.07.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 5, Pages 716–727
DOI: https://doi.org/10.1134/S0001434623110081
Bibliographic databases:
Document Type: Article
MSC: 20К10, 20К12
Language: English
Citation: A. R. Chekhlov, P. V. Danchev, “On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups”, Math. Notes, 114:5 (2023), 716–727
Citation in format AMSBIB
\Bibitem{CheDan23}
\by A.~R.~Chekhlov, P.~V.~Danchev
\paper On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups
\jour Math. Notes
\yr 2023
\vol 114
\issue 5
\pages 716--727
\mathnet{http://mi.mathnet.ru/mzm14093}
\crossref{https://doi.org/10.1134/S0001434623110081}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4680632}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187666010}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    References:4
     
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