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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 74–83 (Mi timm224)  

This article is cited in 4 scientific papers (total in 4 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

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

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S234–S243

Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 10.12.2008

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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\paper On the intersections of solvable Hall subgroups in finite groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\issue 2
\pages 74--83
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S234--S243
\crossref{https://doi.org/10.1134/S0081543809070219}
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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. Vdovin E.P., “On the Base Size of a Transitive Group with Solvable Point Stabilizer”, J. Algebra. Appl., 11:1 (2012), 1250015  crossref  mathscinet  zmath  isi  elib  scopus
    2. E. P. Vdovin, “On intersection of solvable Hall subgroups in finite simple exceptional groups of Lie type”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S183–S190  mathnet  crossref  mathscinet  isi  elib
    3. E. P. Vdovin, “Groups of induced automorphisms and their application to studying the existence problem for Hall subgroups”, Algebra and Logic, 53:5 (2014), 418–421  mathnet  crossref  mathscinet  isi
    4. Guo W., Vdovin E.P., “Number of Sylow Subgroups in Finite Groups”, J. Group Theory, 21:4 (2018), 695–712  crossref  mathscinet  zmath  isi  scopus
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