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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2018, Volume 26, Issue 1, Pages 90–96 (Mi adm672)

RESEARCH ARTICLE

On finite groups with Hall normally embedded Schmidt subgroups

Viktoryia N. Knyahina, Victor S. Monakhov

Department of Mathematics, Francisk Skorina Gomel State University, Sovetskaya str., 104, Gomel 246019, Belarus

Abstract: A subgroup $H$ of a finite group $G$ is said to be Hall normally embedded in $G$ if there is a normal subgroup $N$ of $G$ such that $H$ is a Hall subgroup of $N$. A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if each Schmidt subgroup of a finite group $G$ is Hall normally embedded in $G$, then the derived subgroup of $G$ is nilpotent.

Keywords: finite group, Hall subgroup, normal subgroup, derived subgroup, nilpotent subgroup.

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MSC: 20E28, 20E32, 20E34
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Citation: Viktoryia N. Knyahina, Victor S. Monakhov, “On finite groups with Hall normally embedded Schmidt subgroups”, Algebra Discrete Math., 26:1 (2018), 90–96

Citation in format AMSBIB
\Bibitem{KnyMon18} \by Viktoryia~N.~Knyahina, Victor~S.~Monakhov \paper On finite groups with Hall normally embedded Schmidt subgroups \jour Algebra Discrete Math. \yr 2018 \vol 26 \issue 1 \pages 90--96 \mathnet{http://mi.mathnet.ru/adm672}