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Algebra Discrete Math., 2013, Volume 16, Issue 2, Pages 233–241 (Mi adm450)  

RESEARCH ARTICLE

On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup

V. S. Monakhov, D. V. Gritsuk

Department of Mathematics, Gomel Francisk Skorina State University, Gomel, Belarus

Abstract: It is proved that if $\pi$-Hall subgroup is a supersolvable group then the derived $\pi$-length of a $\pi$-solvable group $G$ is at most $1+ \max_{r\in \pi}l_r^a(G),$ where $l_r^a(G)$ is the derived $r$-length of a $\pi$-solvable group $G.$

Keywords: finite group, $\pi$-soluble group, supersolvable group, $\pi$-Hall subgroup, derived $\pi$-length.

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Bibliographic databases:
MSC: 20D10, 20D20, 20F16
Received: 18.05.2013
Revised: 18.05.2013
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Citation: V. S. Monakhov, D. V. Gritsuk, “On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup”, Algebra Discrete Math., 16:2 (2013), 233–241

Citation in format AMSBIB
\Bibitem{MonGri13}
\by V.~S.~Monakhov, D.~V.~Gritsuk
\paper On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 2
\pages 233--241
\mathnet{http://mi.mathnet.ru/adm450}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3186087}


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