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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 921–928
(Mi semr537)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/semr537 https://www.mathnet.ru/eng/semr/v11/p921
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