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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 3, Pages 159–167 (Mi timm587)  

This article is cited in 2 scientific papers (total in 2 papers)

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

A. V. Konygin

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

Abstract: Assume that $G$ is a primitive permutation group on a finite set $X$, $x\in X$, $y\in X\setminus\{x\}$ and $G_{x,y}\trianglelefteq G_x$. P. Cameron has raised the question about realization of an equality $G_{x,y}=1$ in this case. It is proved that, if (according to the O'Nan–Scott classification) the group $G$ is of type I, type III(a), or type III(c) or $G$ is of type II and $\operatorname{soc}(G)$ is not an exceptional group of Lie type, then $G_{x,y}=1$. In addition, it is proved that, if the group $G$ is of type III(b) and $\operatorname{soc}(G)$ is not a direct product of exceptional groups of Lie type, then $G_{x,y}=1$.

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

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S65–S73

Bibliographic databases:

Document Type: Article
UDC: 512.542.7
Received: 30.04.2010

Citation: 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”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 3, 2010, 159–167; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S65–S73

Citation in format AMSBIB
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\paper 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
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 3
\pages 159--167
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages S65--S73
\crossref{https://doi.org/10.1134/S0081543811020064}
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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. 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  mathnet  crossref  mathscinet  isi  elib
    2. 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  mathnet  mathscinet  elib
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