M. R. Aleeva, “On Finite Simple Groups with the Set of Element Orders as in a Frobenius Group or a Double Frobenius Group”, Mat. Zametki, 73:3 (2003), 323–339; Math. Notes, 73:3 (2003), 299

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Matematicheskie Zametki, 2003, Volume 73, Issue 3, Pages 323–339
DOI: https://doi.org/10.4213/mzm189 (Mi mzm189)

This article is cited in 33 scientific papers (total in 33 papers)

On Finite Simple Groups with the Set of Element Orders as in a Frobenius Group or a Double Frobenius Group

M. R. Aleeva

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Full-text PDF (263 kB) Citations (33)

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DOI: https://doi.org/10.4213/mzm189

Abstract: It is proved that a finite simple group with the set of element orders as in a Frobenius group (a double Frobenius group, respectively) is isomorphic to $L_3(3)$ or $U3_(3)$ (to $U_3(3)$ or $S_4(3)$, respectively).

Received: 05.02.2002

English version:
Mathematical Notes, 2003, Volume 73, Issue 3, Pages 299–313
DOI: https://doi.org/10.1023/A:1023253609066

Bibliographic databases:

UDC: 512.542

Language: Russian

Citation: M. R. Aleeva, “On Finite Simple Groups with the Set of Element Orders as in a Frobenius Group or a Double Frobenius Group”, Mat. Zametki, 73:3 (2003), 323–339; Math. Notes, 73:3 (2003), 299–313

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm189

https://doi.org/10.4213/mzm189

https://www.mathnet.ru/eng/mzm/v73/i3/p323

This publication is cited in the following 33 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
Yuri V. Lytkin, “On finite groups isospectral to the simple group $S_4(3)$”, Sib. elektron. matem. izv., 16 (2019), 1561–1566
Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584
Yu. V. Lytkin, “On finite groups isospectral to $U_3(3)$”, Siberian Math. J., 58:4 (2017), 633–643
V. D. Mazurov, “Neraspoznavaemye po spektru konechnye prostye gruppy i izospektralnye im gruppy”, Vladikavk. matem. zhurn., 17:2 (2015), 47–55
V. D. Mazurov, “$2$-Frobenius groups isospectral to the simple group $U_3(3)$”, Siberian Math. J., 56:6 (2015), 1108–1113
Grechkoseeva M.A., Vasil'ev A.V., “on the Structure of Finite Groups Isospectral To Finite Simple Groups”, J. Group Theory, 18:5 (2015), 741–759
Vasil'ev A.V., “on Finite Groups Isospectral To Simple Classical Groups”, J. Algebra, 423 (2015), 318–374
Yu. V. Lytkin, “On groups critical with respect to a set of natural numbers”, Sib. elektron. matem. izv., 10 (2013), 666–675
M. R. Zinov'eva, V. D. Mazurov, “On finite groups with disconnected prime graph”, Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 139–145
M. R. Zinov'eva, “Recognition by spectrum of simple groups C p (2)”, Proc. Steklov Inst. Math., 279:S1 (2012), 163
M. R. Zinoveva, “Raspoznavanie po spektru prostykh grupp $C_p(2)$”, Tr. IMM UrO RAN, 17, no. 4, 2011, 102–113
Darafsheh M.R., “Recognition of the projective special linear group over GF(3)”, Acta Mathematica Sinica-English Series, 26:3 (2010), 477–488
O. A. Alekseeva, A. S. Kondrat'ev, “On recognizability of some finite simple orthogonal groups by spectrum”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S10–S23
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
A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “Characterization of the finite simple groups by spectrum and order”, Algebra and Logic, 48:6 (2009), 385–409
Kondrat'ev, AS, “Recognition by spectrum of the groups D-2(2m+1)(3)”, Science in China Series A-Mathematics, 52:2 (2009), 293
Moghaddamfar, AR, “A COMPARISON OF THE ORDER COMPONENTS IN Frobenius AND 2-Frobenius GROUPS WITH FINITE SIMPLE GROUPS”, Taiwanese Journal of Mathematics, 13:1 (2009), 67
A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43
O. A. Alekseeva, A. S. Kondratev, “Raspoznavaemost po spektru grupp ${}^2D_p(3)$ dlya nechetnogo prostogo chisla $p$”, Tr. IMM UrO RAN, 14, no. 4, 2008, 3–11

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

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