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Algebra and Discrete Mathematics, 2021, Volume 31, Issue 1, Pages 109–119
DOI: https://doi.org/10.12958/adm1724 (Mi adm791) 		 
RESEARCH ARTICLE

On the structure of some groups having finite contranormal subgroups

L. A. Kurdachenkoa, N. N. Semkob

a Oles Honchar Dnipro National University, Gagarin Avenue 72, 49010, Dnipro, Ukraine
b Department of Mathematics, University of State Fiscal Service of Ukraine, Universitetska 31, 08205, Irpin, Kyiv Region, Ukraine
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DOI: https://doi.org/10.12958/adm1724
Abstract: Following J. S. Rose, a subgroup $H$ of the group $G$ is said to be contranormal in $G$, if $G=H^{G}$. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent groups having a finite proper contranormal $p$-subgroup.
Keywords: contranormal subgroups, Abelian-by-nilpotent groups, hypercenter of a group, $G$-eccentric subgroups, rationally irreducible subgroups.
Funding agency Grant number
National Research Foundation of Ukraine 2020.02/0066
The first author is supported by the National Research Foundation of Ukraine (grant no. 2020.02/0066).
Received: 12.11.2020
Document Type: Article
MSC: 20E99, 20F18, 20F19
Language: English
Citation: L. A. Kurdachenko, N. N. Semko, “On the structure of some groups having finite contranormal subgroups”, Algebra Discrete Math., 31:1 (2021), 109–119
Citation in format AMSBIB
\Bibitem{KurSem21}
\by L.~A.~Kurdachenko, N.~N.~Semko
\paper On the structure of some groups having finite contranormal subgroups
\jour Algebra Discrete Math.
\yr 2021
\vol 31
\issue 1
\pages 109--119
\mathnet{http://mi.mathnet.ru/adm791}
\crossref{https://doi.org/10.12958/adm1724}
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