Abstract:
The spectrum of a group is the set of its element orders. We say that the problem of recognition by spectrum is solved for a finite group if we know the number of pairwise nonisomorphic finite groups with the same spectrum as the group under study. In this article the problem of recognition by spectrum is completely solved for every finite nonabelian simple group with orders having prime divisors at most 13.
Keywords:
recognition by spectrum, finite simple group, group of Lie type.
Citation:
A. V. Vasil'ev, “On recognition of all finite nonabelian simple groups with orders having prime divisors at most 13”, Sibirsk. Mat. Zh., 46:2 (2005), 315–324; Siberian Math. J., 46:2 (2005), 246–253
\Bibitem{Vas05}
\by A.~V.~Vasil'ev
\paper On recognition of all finite nonabelian simple groups with orders having prime divisors at most~13
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 2
\pages 315--324
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\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 2
\pages 246--253
\crossref{https://doi.org/10.1007/s11202-005-0024-z}
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Linking options:
https://www.mathnet.ru/eng/smj966
https://www.mathnet.ru/eng/smj/v46/i2/p315
This publication is cited in the following 15 articles:
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Shi Wujie, “Quantitative characterization of finite simple groups”, Sci. Sin.-Math., 53:7 (2023), 931
M. A. Grechkoseeva, M. A. Zvezdina, “On recognition of l4(q) and u4(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
Liu Sh., “Od-Characterization of Some Alternating Groups”, Turk. J. Math., 39:3 (2015), 395–407
V. D. Mazurov, A. R. Moghaddamfar, “Recognizing by Spectrum for the Automorphism Groups of Sporadic Simple Groups”, Commun. Math. Stat., 3:4 (2015), 491
P. Nosratpour, M. R. Darafsheh, “OD-characterization of all finite nonabelian simple groups with orders having prime divisors at most 13”, Siberian Math. J., 55:4 (2014), 658–666
I. B. Gorshkov, “Thompson's conjecture for simple groups with connected prime graph”, Algebra and Logic, 51:2 (2012), 111–127
M. R. Zinov'eva, “Recognition by spectrum of simple groups C p (2)”, Proc. Steklov Inst. Math., 279:S1 (2012), 163
Bessenrodt Ch., Zhang J., “Character separation and principal covering”, J Algebra, 327:1 (2011), 170–185
M. R. Zinoveva, “Raspoznavanie po spektru prostykh grupp Cp(2)”, Tr. IMM UrO RAN, 17, no. 4, 2011, 102–113
M. R. Zinov'eva, R. Shen, W. Shi, “Recognition of simple groups Bp(3) by the set of element orders”, Siberian Math. J., 51:2 (2010), 244–254
I. B. Gorshkov, “Raspoznavanie po spektru konechnykh prostykh grupp, prostye deliteli poryadkov kotorykh ne prevoskhodyat 17”, Sib. elektron. matem. izv., 7 (2010), 14–20
Zhang Liangcai, Shi Wujie, “OD-characterization of simplex K4-groups”, Algebra Colloq., 16:2 (2009), 275–282
A. V. Vasil'ev, “On connection between the structure of a finite group and the properties of Its prime graph”, Siberian Math. J., 46:3 (2005), 396–404
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