Mathematics of the USSR-Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mathematics of the USSR-Sbornik, 1982, Volume 43, Issue 3, Pages 377–393
DOI: https://doi.org/10.1070/SM1982v043n03ABEH002453
(Mi sm2404)
 

This article is cited in 1 scientific paper (total in 1 paper)

Simple groups with large Sylow subgroups

A. V. Romanovskii
References:
Abstract: A. I. Kostrikin posed the problem of the structure of a simple group having a Sylow $p$-subgroup $P$ for which $|P|^3>|G|$, and $C(x)\subset PC(P)$ whenever $x\in P^\sharp$. It has been established by the author that $PSL(2,q)$, and $Sz(q)$ are the only simple groups of this kind. Earlier Brauer and Reynolds have found the solution to the problem of Artin which is the partial case of Kostrikin's problem when $|P|=p$. One of the results used in the proof of the main theorem of the author leads to the following group-theoretical characterization of $PSL(2,q)$: a simple group $G$ is isomorphic to $PSL(2,q)$, $q>3$, if and only if $G$ contains a $CC$-subgroup of odd order $m$ distinct from its own normalizer in $G$, and such that $|G|<(m+1)^3$.
Bibliography: 28 titles.
Received: 12.12.1980
Bibliographic databases:
UDC: 519.44
MSC: 20D05, 20D20
Language: English
Original paper language: Russian
Citation: A. V. Romanovskii, “Simple groups with large Sylow subgroups”, Math. USSR-Sb., 43:3 (1982), 377–393
Citation in format AMSBIB
\Bibitem{Rom81}
\by A.~V.~Romanovskii
\paper Simple groups with large Sylow subgroups
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 3
\pages 377--393
\mathnet{http://mi.mathnet.ru//eng/sm2404}
\crossref{https://doi.org/10.1070/SM1982v043n03ABEH002453}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=628218}
\zmath{https://zbmath.org/?q=an:0492.20010|0471.20006}
Linking options:
  • https://www.mathnet.ru/eng/sm2404
  • https://doi.org/10.1070/SM1982v043n03ABEH002453
  • https://www.mathnet.ru/eng/sm/v157/i3/p426
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024