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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 1, Pages 30–43 (Mi timm202)  

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

On recognizability of some finite simple orthogonal groups by spectrum

O. A. Alekseevaa, A. S. Kondrat'evb

a Chelyabinsk Institute of Humanities
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: It is proved that if $G$ is a finite group with the same set of element orders as simple group $D_p(q)$, where $p$ is a prime, $p\ge5$ and $q\in\{2,3,5\}$, then the commutator group of $G/F(G)$ is isomorphic to $D_p(q)$, the subgroup $F(G)$ is equal to 1 for $q=5$ and to $O_q(G)$ for $q\in\{2,3\}$, $F(G)\le G'$ and $|G/G'|\le2$.

Keywords: finite simple group, spectrum of a group, prime graph, recognition by spectrum, orthogonal group

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 265, suppl. 1, S10–S23

Bibliographic databases:

UDC: 512.542
Received: 07.02.2009

Citation: O. A. Alekseeva, A. S. Kondrat'ev, “On recognizability of some finite simple orthogonal groups by spectrum”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 30–43; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S10–S23

Citation in format AMSBIB
\Bibitem{AleKon09}
\by O.~A.~Alekseeva, A.~S.~Kondrat'ev
\paper On recognizability of some finite simple orthogonal groups by spectrum
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 1
\pages 30--43
\mathnet{http://mi.mathnet.ru/timm202}
\elib{http://elibrary.ru/item.asp?id=11929775}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 265
\issue , suppl. 1
\pages S10--S23
\crossref{https://doi.org/10.1134/S0081543809060029}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000268192700002}


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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. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “On finite groups isospectral to simple symplectic and orthogonal groups”, Siberian Math. J., 50:6 (2009), 965–981  mathnet  crossref  mathscinet  isi  elib  elib
    2. A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43  mathnet  elib
    3. A. V. Vasil'ev, M. A. Grechkoseeva, “Recognition by spectrum for simple classical groups in characteristic $2$”, Siberian Math. J., 56:6 (2015), 1009–1018  mathnet  crossref  crossref  mathscinet  isi  elib
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