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Algebra Logika, 2009, Volume 48, Number 6, Pages 685–728 (Mi al420)  

This article is cited in 26 scientific papers (total in 26 papers)

Characterization of the finite simple groups by spectrum and order

A. V. Vasil'evab, M. A. Grechkoseevaab, V. D. Mazurovab

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

Abstract: We give an affirmative answer to Question 12.39 in the Kourovka Notebook. Namely, it is proved that a finite simple group and a finite group having equal orders and same sets of element orders are isomorphic.

Keywords: finite group, simple group, element orders, recognizability by spectrum and order, symplectic group, orthogonal group.

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English version:
Algebra and Logic, 2009, 48:6, 385–409

Bibliographic databases:

UDC: 512.542
Received: 05.08.2009

Citation: A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “Characterization of the finite simple groups by spectrum and order”, Algebra Logika, 48:6 (2009), 685–728; Algebra and Logic, 48:6 (2009), 385–409

Citation in format AMSBIB
\by A.~V.~Vasil'ev, M.~A.~Grechkoseeva, V.~D.~Mazurov
\paper Characterization of the finite simple groups by spectrum and order
\jour Algebra Logika
\yr 2009
\vol 48
\issue 6
\pages 685--728
\jour Algebra and Logic
\yr 2009
\vol 48
\issue 6
\pages 385--409

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    2. A. S. Kondrat'ev, “Finite groups having the same prime graph as the group $Aut(J_2)$”, Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 78–85  mathnet  crossref  isi  elib
    3. Ghasemabadi M.F., Iranmanesh A., “2-Quasirecognizability of the Simple Groups B-N(P) and C-N(P) by Prime Graph”, Bull. Iran Math. Soc., 38:3 (2012), 647–668  mathscinet  zmath  isi
    4. Shen H., Cao H., Chen G., “Characterization of Automorphism Groups of Sporadic Simple Groups”, Front. Math. China, 7:3 (2012), 513–519  crossref  mathscinet  zmath  isi  elib  scopus
    5. He L.-G., Chen G.-Yu., “A New Characterization of Simple K-3-Groups”, Commun. Algebr., 40:10 (2012), 3903–3911  crossref  mathscinet  zmath  isi  elib  scopus
    6. Ghasemabadi M.F., Iranmanesh A., Ahanjideh N., “Characterizations of the Simple Group D-2(N)(3) by Prime Graph and Spectrum”, Mon.heft. Math., 168:3-4 (2012), 347–361  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. Momen Z., Khosravi B., “On R-Recognition by Prime Graph of B (P) (3) Where P Is an Odd Prime”, Mon.heft. Math., 166:2 (2012), 239–253  crossref  mathscinet  zmath  isi  scopus
    9. Z. Momen, B. Khosravi, “Groups with the same prime graph as the orthogonal group $B_n(3)$”, Siberian Math. J., 54:3 (2013), 487–500  mathnet  crossref  mathscinet  isi
    10. 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
    11. Momen Z. Khosravi B., “Groups With the Same Orders of Maximal Abelian Subgroups as a(2)(Q)”, Mon.heft. Math., 174:2 (2014), 285–303  crossref  mathscinet  zmath  isi  scopus
    12. Al-Hasanat B., Ahmad A., Sulaiman H., “Order Classes of Dihedral Groups”, Proceedings of the 21St National Symposium on Mathematical Sciences (Sksm21): Germination of Mathematical Sciences Education and Research Towards Global Sustainability, AIP Conference Proceedings, 1605, eds. Ismail M., Ahmad S., Rahman R., Amer Inst Physics, 2014, 551–556  crossref  isi  scopus
    13. M. F. Ghasemabadi, A. Iranmanesh, F. Mavadatpour, “A new characterization of some finite simple groups”, Siberian Math. J., 56:1 (2015), 78–82  mathnet  crossref  mathscinet  isi  elib  elib
    14. 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
    15. Yan Ya., Xu H., Chen G., “Od-Characterization of Alternating and Symmetric Groups of Degree P+5”, Chin. Ann. Math. Ser. B, 36:6 (2015), 1001–1010  crossref  mathscinet  zmath  isi  elib  scopus
    16. Vasil'ev A.V., “on Finite Groups Isospectral To Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    17. Li J., Shi W., Yu D., “a Characterization of Some Pgl(2, Q) By Maximum Element Orders”, Bull. Korean. Math. Soc., 52:6 (2015), 2025–2034  crossref  mathscinet  zmath  isi  elib  scopus
    18. Jiang Q., Shao Ch., “Characterization of Some l-2(Q) By the Largest Element Orders”, Math. Rep., 17:4 (2015), 353–358  mathscinet  zmath  isi  elib
    19. 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
    20. Chen Ya., Chen G., Li J., “Recognizing Simple K-4-Groups By Few Special Conjugacy Class Sizes”, Bull. Malays. Math. Sci. Soc., 38:1 (2015), 51–72  crossref  mathscinet  zmath  isi  scopus
    21. M. A. Grechkoseeva, D. V. Lytkin, “On maximum orders of elements of simple orthogonal groups in characteristic 2”, Sib. elektron. matem. izv., 14 (2017), 405–417  mathnet  crossref
    22. Staroletov A., “On Almost Recognizability By Spectrum of Simple Classical Groups”, Int. J. Group Theory, 6:4 (2017), 7–33  crossref  mathscinet  isi
    23. Jiang Q.H., Shao C.G., Shi W.J., Zhang Q.L., “A New Characterization of l-2(Q) By the Largest Element Orders”, Bull. Iran Math. Soc., 43:5 (2017), 1143–1151  mathscinet  isi
    24. Li J., Yu D., Chen G., Shi W., “A Characterization of Simple K-4-Groups of Type l-2(Q) and Their Automorphism Groups”, Bull. Iran Math. Soc., 43:2 (2017), 501–514  mathscinet  isi
    25. Momen Z., Khosravi B., “Quasirecognition of E-6(Q) By the Orders of Maximal Abelian Subgroups”, J. Algebra. Appl., 17:7 (2018), 1850122  crossref  mathscinet  zmath  isi  scopus
    26. E. Jabara, A. Zakavi, “Periodic groups whose all involutions are odd transpositions”, Siberian Math. J., 60:1 (2019), 178–184  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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