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Tr. Inst. Mat., 2012, Volume 20, Number 2, Pages 3–9 (Mi timb168)  

This article is cited in 1 scientific paper (total in 1 paper)

On solvable groups whose Sylow subgroups are either abelian or extraspecial

D. V. Gritsuk, V. S. Monakhov

Francisk Skaryna Gomel State University, Faculty of Mathematics

Abstract: A $p$-group $G$ is called extraspecial if its derived subgroup, center and Frattini subgroup are groups of order $p.$ We consider the solvable groups whose Sylow subgroups are either abelian or extraspecial. It is proved that derived length is at most $2\cdot|\pi(G)|$ and nilpotent length is at most $2+|\pi(G)|$.

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UDC: 512.542
Received: 12.11.2012

Citation: D. V. Gritsuk, V. S. Monakhov, “On solvable groups whose Sylow subgroups are either abelian or extraspecial”, Tr. Inst. Mat., 20:2 (2012), 3–9

Citation in format AMSBIB
\Bibitem{GriMon12}
\by D.~V.~Gritsuk, V.~S.~Monakhov
\paper On solvable groups whose Sylow subgroups are either abelian or extraspecial
\jour Tr. Inst. Mat.
\yr 2012
\vol 20
\issue 2
\pages 3--9
\mathnet{http://mi.mathnet.ru/timb168}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Gritsuk, “Proizvodnaya $\pi$-dlina $\pi$-razreshimoi gruppy, silovskie $p$-podgruppy kotoroi libo bitsiklicheskie, libo imeyut poryadok $p^3$”, PFMT, 2014, no. 2(19), 54–58  mathnet
  • Труды Института математики
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