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Algebra and Discrete Mathematics, 2012, Volume 14, Issue 1, Pages 84–106 (Mi adm86)  
This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

Groups with many pronormal and transitively normal subgroups

L. A. Kurdachenkoa, N. N. Semko (Jr.)b, I. Ya. Subbotinc

a Department of Algebra, National University of Dnepropetrovsk, Vul. Naukova 13, Dnepropetrovsk 50, Ukraine 49050
b Department of Mathematics, National University of The State Tax Service of Ukraine, Irpen, Ukraine
c Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA
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Abstract: A subgroup $H$ of a group $G$ is said to be transitively normal in $G$, if $H$ is normal in every subgroup $K\geqslant H$ such that $H$ is subnormal in $K$. We described some infinite groups, whose non–finitely generated subgroups are transitively normal.
Keywords: soluble group, radical group, locally nilpotent group, transitively normal subgroup, non finitely generated subgroup.
Received: 29.05.2012
Accepted: 29.05.2012
Bibliographic databases:
Document Type: Article
MSC: 20E15, 20F19
Language: English
Citation: L. A. Kurdachenko, N. N. Semko (Jr.), I. Ya. Subbotin, “Groups with many pronormal and transitively normal subgroups”, Algebra Discrete Math., 14:1 (2012), 84–106
Citation in format AMSBIB
\Bibitem{KurSemSub12}
\by L.~A.~Kurdachenko, N.~N.~Semko (Jr.), I.~Ya.~Subbotin
\paper Groups with many pronormal and transitively normal subgroups
\jour Algebra Discrete Math.
\yr 2012
\vol 14
\issue 1
\pages 84--106
\mathnet{http://mi.mathnet.ru/adm86}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3052323}
\zmath{https://zbmath.org/?q=an:1294.20036}
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    		Algebra and Discrete Mathematics
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