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Tr. Inst. Mat., 2008, Volume 16, Number 1, Pages 64–66 (Mi timb56)  

This article is cited in 3 scientific papers (total in 3 papers)

Towards Huppert–Shemetkov's theorem

V. S. Monakhov

Francisk Skorina Gomel State University

Abstract: It is proved that in every finite non-identity soluble group $G$ there exists a maximal subgroup $H$ such that $H$ does not contain the Fitting subgroup and $|G:H|=p^{r(G/\Phi(G))}$ for some prime number $p$. Here $r(G/\Phi(G))$ is the chief rank of the quotient $G/\Phi(G)$.

Full text: PDF file (188 kB)
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UDC: 512.542
Received: 03.01.2008

Citation: V. S. Monakhov, “Towards Huppert–Shemetkov's theorem”, Tr. Inst. Mat., 16:1 (2008), 64–66

Citation in format AMSBIB
\Bibitem{Mon08}
\by V.~S.~Monakhov
\paper Towards Huppert--Shemetkov's theorem
\jour Tr. Inst. Mat.
\yr 2008
\vol 16
\issue 1
\pages 64--66
\mathnet{http://mi.mathnet.ru/timb56}


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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. A. Trofimuk, “Derived Length of Finite Groups with Restrictions on Sylow Subgroups”, Math. Notes, 87:2 (2010), 264–270  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. S. Monakhov, A. A. Trofimuk, “Invarianty konechnykh razreshimykh grupp”, PFMT, 2010, no. 1(2), 63–81  mathnet
    3. A. A. Trofimuk, “O fittingovykh podgruppakh konechnoi razreshimoi gruppy”, Tr. IMM UrO RAN, 18, no. 3, 2012, 242–246  mathnet  elib
  • Труды Института математики
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