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 Trudy Inst. Mat. i Mekh. UrO RAN, 2007, Volume 13, Number 2, Pages 86–89 (Mi timm91)

On intersections of solvable Hall subgroups in finite nonsolvable groups

V. I. Zenkov

Abstract: The author continues the investigation of intersections of Hall subgroups in finite groups. Previously, the author proved that in the case when a Hall subgroup is Sylow there are three subgroups conjugate to it such that their intersection coincides with the maximal normal primary subgroup. A similar assertion holds for Hall subgroups in solvable groups. The aim of this paper is to construct examples of a (nonsolvable) group in which the intersection of any four subgroups conjugate to some Hall subgroup is nontrivial.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2007, 259, suppl. 2, S250–S253

Document Type: Article
UDC: 512.54

Citation: V. I. Zenkov, “On intersections of solvable Hall subgroups in finite nonsolvable groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 86–89; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S250–S253

Citation in format AMSBIB
\Bibitem{Zen07} \by V.~I.~Zenkov \paper On intersections of solvable Hall subgroups in finite nonsolvable groups \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2007 \vol 13 \issue 2 \pages 86--89 \mathnet{http://mi.mathnet.ru/timm91} \elib{http://elibrary.ru/item.asp?id=12040771} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2007 \vol 259 \issue , suppl. 2 \pages S250--S253 \crossref{https://doi.org/10.1134/S0081543807060181} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38949123180} 

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This publication is cited in the following articles:
1. E. P. Vdovin, V. I. Zenkov, “On the intersections of solvable Hall subgroups in finite groups”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S234–S243
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
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