A. V. Vasil'ev, M. A. Grechkoseeva, A. M. Staroletov, “On finite groups isospectral to simple linear and unitary groups”, Sibirsk. Mat. Zh., 52:1 (2011), 39–53; Siberian Math. J., 52:1 (2011), 30

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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 1, Pages 39–53 (Mi smj2176)

This article is cited in 11 scientific papers (total in 11 papers)

On finite groups isospectral to simple linear and unitary groups

A. V. Vasil'ev^ab, M. A. Grechkoseeva^ab, A. M. Staroletov^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

Full-text PDF (387 kB) Citations (11)

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Abstract: Let $L$ be a simple linear or unitary group of dimension larger than 3 over a finite field of characteristic $p$. We deal with the class of finite groups isospectral to $L$. It is known that a group of this class has a unique nonabelian composition factor. We prove that if $L\ne U_4(2),U_5(2)$ then this factor is isomorphic to either $L$ or a group of Lie type over a field of characteristic different from $p$.

Keywords: finite group, spectrum of a group, simple group, linear group, unitary group, composition factor.

Received: 23.03.2010

English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 1, Pages 30–40
DOI: https://doi.org/10.1134/S0037446606010046

Bibliographic databases:

Document Type: Article

UDC: 512.542

Language: Russian

Citation: A. V. Vasil'ev, M. A. Grechkoseeva, A. M. Staroletov, “On finite groups isospectral to simple linear and unitary groups”, Sibirsk. Mat. Zh., 52:1 (2011), 39–53; Siberian Math. J., 52:1 (2011), 30–40

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj2176

https://www.mathnet.ru/eng/smj/v52/i1/p39

This publication is cited in the following 11 articles:

Maria A. Grechkoseeva, Victor D. Mazurov, Wujie Shi, Andrey V. Vasil'ev, Nanying Yang, “Finite Groups Isospectral to Simple Groups”, Commun. Math. Stat., 11:2 (2023), 169
M. A. Grechkoseeva, M. A. Zvezdina, “On recognition of $l_4(q)$ and $u_4(q)$ by spectrum”, Siberian Math. J., 61:6 (2020), 1039–1065
Yang N. Grechkoseeva M.A. Vasil'ev A.V., “on the Nilpotency of the Solvable Radical of a Finite Group Isospectral to a Simple Group”, J. Group Theory, 23:3 (2020), 447–470
Grechkoseeva M.A. Vasil'ev A.V. Zvezdina M.A., “Recognition of Symplectic and Orthogonal Groups of Small Dimensions By Spectrum”, J. Algebra. Appl., 18:12 (2019), 1950230
M. A. Grechkoseeva, “On spectra of almost simple extensions of even-dimensional orthogonal groups”, Siberian Math. J., 59:4 (2018), 623–640
Staroletov A., “On Almost Recognizability By Spectrum of Simple Classical Groups”, Int. J. Group Theory, 6:4 (2017), 7–33
Wei Dong, Baogang Xu, “2-Distance coloring of planar graphs with girth 5”, J Comb Optim, 34:4 (2017), 1302
A. V. Vasil'ev, A. M. Staroletov, “Almost recognizability by spectrum of simple exceptional groups of Lie type”, Algebra and Logic, 53:6 (2015), 433–449
M. A. Zvezdina, “On nonabelian simple groups having the same prime graph as an alternating group”, Siberian Math. J., 54:1 (2013), 47–55
M. A. Grechkoseeva, D. V. Lytkin, “Almost recognizability by spectrum of finite simple linear groups of prime dimension”, Siberian Math. J., 53:4 (2012), 645–655
A. M. Staroletov, “Sporadic composition factors of finite groups isospectral to simple groups”, Sib. elektron. matem. izv., 8 (2011), 268–272

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	91
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