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Sibirsk. Mat. Zh., 2004, Volume 45, Number 3, Pages 510–526 (Mi smj1086)  

This article is cited in 31 scientific papers (total in 31 papers)

On recognition of the finite simple orthogonal groups of dimension $2^m$, $2^m+1$ and $2^m+2$ over a field of characteristic 2

A. V. Vasil'eva, M. A. Grechkoseevab

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

Abstract: The spectrum $\omega(G)$ of a finite group $G$ is the set of element orders of $G$. A finite group $G$ is said to be recognizable by spectrum (briefly, recognizable) if $H\simeq G$ for every finite group $H$ such that $\omega(H)=\omega(G)$. We give two series, infinite by dimension, of finite simple classical groups recognizable by spectrum.

Keywords: recognition by spectrum, finite orthogonal group

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English version:
Siberian Mathematical Journal, 2004, 45:3, 420–432

Bibliographic databases:

UDC: 512.542
Received: 29.12.2003

Citation: A. V. Vasil'ev, M. A. Grechkoseeva, “On recognition of the finite simple orthogonal groups of dimension $2^m$, $2^m+1$ and $2^m+2$ over a field of characteristic 2”, Sibirsk. Mat. Zh., 45:3 (2004), 510–526; Siberian Math. J., 45:3 (2004), 420–432

Citation in format AMSBIB
\by A.~V.~Vasil'ev, M.~A.~Grechkoseeva
\paper On recognition of the finite simple orthogonal groups of dimension $2^m$, $2^m+1$ and $2^m+2$ over a field of characteristic~2
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 3
\pages 510--526
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 3
\pages 420--432

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    This publication is cited in the following articles:
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    2. 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  mathnet  crossref  mathscinet  zmath  isi  elib
    3. O. A. Alekseeva, “Quasirecognizability by the Set of Element Orders for Groups ${^3}D_4(q)$, for $q$ Even”, Algebra and Logic, 45:1 (2006), 1–11  mathnet  crossref  mathscinet  zmath  elib  elib
    4. Mazurov V.D., Moghaddamfar A.R., “The recognition of the simple group $S_8(2)$ by its spectrum”, Algebra Colloq., 13:4 (2006), 643–646  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. S. Kondrat'ev, “Quasirecognition by the set of element orders of the groups $E_6(q)$ and $^2E_6(q)$”, Siberian Math. J., 48:6 (2007), 1001–1018  mathnet  crossref  mathscinet  zmath  isi  elib
    6. A. Khosravi, B. Khosravi, “Quasirecognition by prime graph of the simple group $^2G_2(q)$”, Siberian Math. J., 48:3 (2007), 570–577  mathnet  crossref  mathscinet  zmath  isi  elib
    7. A. Khosravi, B. Khosravi, “2-Recognizability by prime graph of $PSL(2,p^2)$”, Siberian Math. J., 49:4 (2008), 749–757  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. 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  mathnet  elib
    9. 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  mathnet  crossref  isi  elib
    10. A. V. Vasil'ev, I. B. Gorshkov, M. A. Grechkoseeva, A. S. Kondrat'ev, A. M. Staroletov, “On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and $ ^2D_n$ for$n=2^k$”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S218–S233  mathnet  crossref  isi  elib
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    12. Babai A., Khosravi B., Hasani N., “Quasirecognition by prime graph of $ ^2D_p(3)$ where $p=2^n+1\ge 5$ is a prime”, Bull. Malays. Math. Sci. Soc. (2), 32:3 (2009), 343–350  mathscinet  zmath  isi
    13. He Huaiyu, Shi Wujie, “Recognition of some finite simple groups of type $D_n(q)$ by spectrum”, Internat. J. Algebra Comput., 19:5 (2009), 681–698  crossref  mathscinet  zmath  isi  scopus
    14. Kondrat'ev A.S., “Recognition by spectrum of the groups $^2D_{2^m+1}(3)$”, Sci. China Ser. A, 52:2 (2009), 293–300  crossref  mathscinet  zmath  isi  scopus
    15. Akhlaghi Z., Khatami M., Khosravi B., “Quasirecognition by prime graph of the simple group $ ^2F_4(q)$”, Acta Math. Hungar., 122:4 (2009), 387–397  crossref  mathscinet  zmath  isi  elib  scopus
    16. A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43  mathnet  elib
    17. Zhang Q., Shi W., Shen R., “Quasirecognition by Prime Graph of the Simple Groups G(2)(Q) and B-2(2)(Q)”, J Algebra Appl, 10:2 (2011), 309–317  crossref  mathscinet  zmath  isi  elib  scopus
    18. Khosravi B., Babai A., “Quasirecognition by prime graph of F (4)(q) where q=2 (n) > 2”, Monatsh Math, 162:3 (2011), 289–296  crossref  mathscinet  zmath  isi  elib  scopus
    19. A. Babai, B. Khosravi, “Recognition by prime graph of $^2D_{2m+1}(3)$”, Siberian Math. J., 52:5 (2011), 788–795  mathnet  crossref  mathscinet  isi
    20. He H. Shi W., “A Note on the Adjacency Criterion for the Prime Graph and the Characterization of C-P(3)”, Algebr. Colloq., 19:3 (2012), 553–562  crossref  mathscinet  zmath  isi  elib
    21. Babai A. Khosravi B., “On the Composition Factors of a Group with the Same Prime Graph as B (N) (5)”, Czech. Math. J., 62:2 (2012), 469–486  crossref  mathscinet  zmath  isi  elib  scopus
    22. Khosravi B. Moradi H., “Quasirecognition by Prime Graph of Some Orthogonal Groups Over the Binary Field”, J. Algebra. Appl., 11:3 (2012), 1250056  crossref  mathscinet  zmath  isi  elib  scopus
    23. A. Babai, B. Khosravi, “Quasirecognition by Prime Graph of $^2D_{n}(3^\alpha)$ where $n=4m+1\ge 21$ and $\alpha$ is Odd”, Math. Notes, 95:3 (2014), 293–303  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    24. Babai A., Khosravi B., “Groups With the Same Prime Graph as the Simple Group D (N) (5)”, Ukr. Math. J., 66:5 (2014), 666–677  crossref  mathscinet  zmath  isi  elib  scopus
    25. A. V. Vasil'ev, M. A. Grechkoseeva, “Recognition by spectrum for simple classical groups in characteristic $2$”, Siberian Math. J., 56:6 (2015), 1009–1018  mathnet  crossref  crossref  mathscinet  isi  elib
    26. Grechkoseeva M.A., “Element Orders in Covers of Finite Simple Groups of Lie Type”, J. Algebra. Appl., 14:4 (2015), 1550056  crossref  mathscinet  zmath  isi  elib  scopus
    27. Babai A., Khosravi B., “Quasirecognition By Prime Graph of l-N(2(Alpha)) For Some N and Alpha”, Math. Rep., 17:1 (2015), 119–132  mathscinet  zmath  isi  elib
    28. Khosravi B. Babai A., “Simple Groups With the Same Prime Graph as D-N(Q)”, Bull. Iran Math. Soc., 42:6 (2016), 1403–1427  mathscinet  zmath  isi
    29. Ghasemabadi M.F. Iranmanesh A., “Simple Groups With M-Regular First Prime Graph Component”, Hacet. J. Math. Stat., 45:3 (2016), 705–716  crossref  mathscinet  zmath  isi  scopus
    30. Babai A. Khatami M., “a New Characterization of a(P) (2) and a(P-1) (2) Where 2(P)-1 Is a Prime”, Math. Rep., 21:4 (2019), 431–440  mathscinet  zmath  isi
    31. A. M. Staroletov, “O kompozitsionnykh faktorakh konechnykh grupp, izospektralnykh prostym klassicheskim gruppam”, Sib. matem. zhurn., 62:2 (2021), 422–440  mathnet  crossref
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