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Algebra Discrete Math., 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

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.

Full text: PDF file (260 kB)
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Bibliographic databases:
MSC: 20E15, 20F19
Received: 29.05.2012
Accepted:29.05.2012
Language:

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://www.ams.org/mathscinet-getitem?mr=3052323}
\zmath{https://zbmath.org/?q=an:1294.20036}


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    This publication is cited in the following articles:
    1. N. N. Semko (Jr.), “Groups with many pronormal and transitively normal subgroups”, Algebra Discrete Math., 15:2 (2013), 269–286  mathnet  mathscinet
  • Algebra and Discrete Mathematics
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