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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 921–928 (Mi semr537)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematical logic, algebra and number theory

Unrecognizability by spectrum of finite simple orthogonal groups of dimension nine

M. A. Grechkoseevaab, A. M. Staroletovab

a Sobolev Institute of Mathematics, Ac. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia
Full-text PDF (527 kB) Citations (4)
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Abstract: The spectrum of a finite group is the set of its elements orders. A group $G$ is said to be unrecognizable by spectrum if there are infinitely many pairwise non-isomorphic finite groups having the same spectrum as $G$. We prove that the simple orthogonal group $O_9(q)$ has the same spectrum as $V\rtimes O_8^-(q)$ where $V$ is the natural 8-dimensional module of the simple orthogonal group $O_8^-(q)$, and in particular $O_9(q)$ is unrecognizable by spectrum. Note that for $q=2$, the result was proved earlier by Mazurov and Moghaddamfar.
Keywords: spectrum, element order, orthogonal group, finite simple group.
Received November 28, 2014, published December 5, 2014
Document Type: Article
UDC: 512.542
MSC: 20D06, 20D60
Language: English
Citation: M. A. Grechkoseeva, A. M. Staroletov, “Unrecognizability by spectrum of finite simple orthogonal groups of dimension nine”, Sib. Èlektron. Mat. Izv., 11 (2014), 921–928
Citation in format AMSBIB
\Bibitem{GreSta14}
\by M.~A.~Grechkoseeva, A.~M.~Staroletov
\paper Unrecognizability by spectrum of finite simple orthogonal groups of~dimension nine
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 921--928
\mathnet{http://mi.mathnet.ru/semr537}
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  • This publication is cited in the following 4 articles:
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