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 Sib. Èlektron. Mat. Izv., 2008, Volume 5, Pages 387–406 (Mi semr114)

Research papers

On primitive permutation groups

A. V. Konygin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Let $G$ be a primitive permutation group on a finite set $X$, $x\in X,$ $y\in X\setminus\{y\}$ and $G_{xy}\unlhd G_x$. It is proved that, if $G$ is of type I, type III(a), type III(c) (of the O'Nan–Scott classification) or $G$ is of type II and $\operatorname{soc}(G)$ is not an exceptional group of Lie type or a sporadic simple group, then $G_{xy}=1$. In addition, it is proved that if $G$ is of type III(b) and $\operatorname{soc}(G)$ is not a direct product of exceptional groups of Lie type or sporadic simple groups, then $G_{xy}=1$.

Keywords: primitive permutation group, O'Nan–Scott classification.

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Bibliographic databases:

Document Type: Article
UDC: 512.542.7
MSC: 20B15
Received September 18, 2008, published October 2, 2008

Citation: A. V. Konygin, “On primitive permutation groups”, Sib. Èlektron. Mat. Izv., 5 (2008), 387–406

Citation in format AMSBIB
\Bibitem{Kon08} \by A.~V.~Konygin \paper On primitive permutation groups \jour Sib. \Elektron. Mat. Izv. \yr 2008 \vol 5 \pages 387--406 \mathnet{http://mi.mathnet.ru/semr114} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586645} `

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This publication is cited in the following articles:
1. A. V. Konygin, “On primitive permutation groups with a stabilizer of two points that is normal in the stabilizer of one of them: case when the socle is a power of sporadic simple group”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S65–S73
2. A. V. Konygin, “On Cameron's question about primitive permutation groups with stabilizer of two points that is normal in the stabilizer of one of them”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S116–S127
3. A. V. Konygin, “K voprosu Kamerona o trivialnosti v primitivnykh gruppakh podstanovok stabilizatora dvukh tochek, normalnogo v stabilizatore odnoi iz nikh”, Tr. IMM UrO RAN, 21, no. 3, 2015, 175–186
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