RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 3 scientific papers (total in 3 papers)

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.

Full text: PDF file (840 kB)
References: PDF file   HTML file

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}


Linking options:
  • http://mi.mathnet.ru/eng/semr114
  • http://mi.mathnet.ru/eng/semr/v5/p387

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  isi  elib
    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  mathnet  crossref  mathscinet  isi  elib
    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  mathnet  mathscinet  elib
  • Number of views:
    This page:119
    Full text:39
    References:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019