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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 3(7), Pages 426–444 (Mi msb2404)  

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

Simple groups with large Sylow subgroups

A. V. Romanovskii


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.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:3, 377–393

Bibliographic databases:

UDC: 519.44
MSC: 20D05, 20D20
Received: 12.12.1980

Citation: A. V. Romanovskii, “Simple groups with large Sylow subgroups”, Mat. Sb. (N.S.), 115(157):3(7) (1981), 426–444; 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 Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 3(7)
\pages 426--444
\mathnet{http://mi.mathnet.ru/msb2404}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=628218}
\zmath{https://zbmath.org/?q=an:0492.20010|0471.20006}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 3
\pages 377--393
\crossref{https://doi.org/10.1070/SM1982v043n03ABEH002453}


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    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. Romanovskii, “A characterization of simple Zassenhaus groups”, Math. USSR-Sb., 47:2 (1984), 397–409  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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