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Mat. Sb. (N.S.), 1979, Volume 109(151), Number 2(6), Pages 203–228 (Mi msb2366)  

Finite simple groups whose Sylow $2$-subgroups contain a cyclic subgroup of index $16$

È. M. Pal'chik


Abstract: In the paper the following main result is proved.
Theorem.Let $X$ be a finite simple group with Sylow $2$-subgroup $P$. Suppose that $P$ has a cyclic subgroup of index $16$. Then either the sectional $2$-rank of $X$ does not exceed $4$, or $|P|\leqslant2^8$, or $X\cong L_2(32)$.
A use of results of Gorenstein and Harada (RZh.Mat., 1975, 5A192), Kondrat'ev (RZh.Mat., 1977, 12A192), Beisiegel (RZh.Mat., 1977, 12A191) and Volker Stingl leads to the conclusion that finite simple groups whose $2$-subgroups have a cyclic subgroup of index $16$ are known.
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Sbornik, 1980, 37:2, 181–203

Bibliographic databases:

UDC: 519.44
MSC: 20D06, 20D20
Received: 16.07.1976 and 07.08.1978

Citation: È. M. Pal'chik, “Finite simple groups whose Sylow $2$-subgroups contain a cyclic subgroup of index $16$”, Mat. Sb. (N.S.), 109(151):2(6) (1979), 203–228; Math. USSR-Sb., 37:2 (1980), 181–203

Citation in format AMSBIB
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\by \`E.~M.~Pal'chik
\paper Finite simple groups whose Sylow $2$-subgroups contain a~cyclic subgroup of index~$16$
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 109(151)
\issue 2(6)
\pages 203--228
\mathnet{http://mi.mathnet.ru/msb2366}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=542558}
\zmath{https://zbmath.org/?q=an:0446.20010|0422.20011}
\transl
\jour Math. USSR-Sb.
\yr 1980
\vol 37
\issue 2
\pages 181--203
\crossref{https://doi.org/10.1070/SM1980v037n02ABEH001949}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KQ02900003}


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