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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 2, Pages 74–83 (Mi timm224)  

This article is cited in 6 scientific papers (total in 6 papers)

On the intersections of solvable Hall subgroups in finite groups

E. P. Vdovin, V. I. Zenkov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (199 kB) Citations (6)
References:
Abstract: The following conjecture is considered: if a finite group $G$ possesses a solvable $\pi$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_\pi(G)$ holds. Under additional conditions on $G$ and $H$, it is shown that a minimal counterexample to this conjecture must be an almost simple group of Lie type.
Keywords: solvable Hall subgroup, finite simple group, $\pi$-radical.
Received: 10.12.2008
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, Volume 267, Issue 1, Pages S234–S243
DOI: https://doi.org/10.1134/S0081543809070219
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: E. P. Vdovin, V. I. Zenkov, “On the intersections of solvable Hall subgroups in finite groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 74–83; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S234–S243
Citation in format AMSBIB
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\by E.~P.~Vdovin, V.~I.~Zenkov
\paper On the intersections of solvable Hall subgroups in finite groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 74--83
\mathnet{http://mi.mathnet.ru/timm224}
\elib{https://elibrary.ru/item.asp?id=12878770}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S234--S243
\crossref{https://doi.org/10.1134/S0081543809070219}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000274041900021}
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  • https://www.mathnet.ru/eng/timm224
  • https://www.mathnet.ru/eng/timm/v15/i2/p74
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Full-text PDF :108
    References:91
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