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Algebra Logika, 2011, Volume 50, Number 4, Pages 425–470 (Mi al495)  

This article is cited in 45 scientific papers (total in 45 papers)

Cocliques of maximal size in the prime graph of a finite simple group

A. V. Vasil'evab, E. P. Vdovinab

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

Abstract: A prime graph of a finite group is defined in the following way: the set of vertices of the graph is the set of prime divisors of the order of the group, and two distinct vertices $r$ and $s$ are joined by an edge if there is an element of order $rs$ in the group. We describe all cocliques of maximal size for finite simple groups.

Keywords: finite simple group, group of Lie type, prime graph, coclique.

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English version:
Algebra and Logic, 2011, 50:4, 291–322

Bibliographic databases:

UDC: 512.542
Received: 01.10.2010
Revised: 17.03.2011

Citation: A. V. Vasil'ev, E. P. Vdovin, “Cocliques of maximal size in the prime graph of a finite simple group”, Algebra Logika, 50:4 (2011), 425–470; Algebra and Logic, 50:4 (2011), 291–322

Citation in format AMSBIB
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\pages 425--470
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
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    5. M. A. Grechkoseeva, W. J. Shi, “On finite groups isospectral to finite simple unitary groups over fields of characteristic 2”, Sib. elektron. matem. izv., 10 (2013), 31–37  mathnet
    6. A. V. Zavarnitsine, “Finite groups with a five-component prime graph”, Siberian Math. J., 54:1 (2013), 40–46  mathnet  crossref  mathscinet  isi
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    13. Xu MingChun, Shi WuJie, “Thompson's conjecture for Lie type groups $E_7(q)$”, Sci. China-Math., 57:3 (2014), 499–514  crossref  mathscinet  zmath  isi  scopus
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    15. M. A. Zvezdina, “Spectra of automorphic extensions of finite simple symplectic and orthogonal groups over fields of characteristic 2”, Sib. elektron. matem. izv., 11 (2014), 823–832  mathnet
    16. 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  mathnet  crossref  mathscinet  isi
    17. I. B. Gorshkov, “Recognizability of symmetric groups by spectrum”, Algebra and Logic, 53:6 (2015), 450–457  mathnet  crossref  mathscinet  isi
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    24. 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
    25. M. A. Grechkoseeva, A. V. Vasil'ev, “On the structure of finite groups isospectral to finite simple groups”, J. Group Theory, 18:5 (2015), 741–759  crossref  mathscinet  zmath  isi  elib  scopus
    26. Z. Momen, B. Khosravi, “Quasirecognition by prime graph of the simple group $B_n(9)$”, Proc. Rom. Acad. Ser. A-Math. Phys., 16:3 (2015), 397–404  mathscinet  zmath  isi  elib
    27. M. A. Grechkoseeva, “Element orders in covers of finite simple groups of Lie type”, J. Algebra. Appl., 14:4 (2015), 1550056  crossref  mathscinet  zmath  isi  elib  scopus
    28. A. V. Vasil'ev, “On finite groups isospectral to simple classical groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    29. A. Mahmoudifar, B. Khosravi, “On quasirecognition by prime graph of the simple groups $A_n^+(p)$ and $A_n^-(p)$”, J. Algebra. Appl., 14:1 (2015), 1550006  crossref  mathscinet  zmath  isi  elib  scopus
    30. B. Akbari, A. R. Moghaddamfar, “OD-characterization of certain four dimensional linear groups with related results concerning degree patterns”, Front. Math. China, 10:1 (2015), 1–31  crossref  mathscinet  zmath  isi  elib  scopus
    31. A. Babai, B. Khosravi, “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
    32. N. V. Maslova, D. Pagon, “On the realizability of a graph as the Gruenberg–Kegel graph of a finite group”, Sib. elektron. matem. izv., 13 (2016), 89–100  mathnet  crossref
    33. A. S. Kondrat'ev, “Finite groups with given properties of their prime graphs”, Algebra and Logic, 55:1 (2016), 77–82  mathnet  crossref  crossref  isi  elib
    34. M. R. Zinov'eva, “On finite simple classical groups over fields of different characteristics with coinciding prime graphs”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 223–239  mathnet  crossref  crossref  mathscinet  isi  elib
    35. M. A. Zvezdina, “Spectra of automorphic extensions of finite simple exceptional groups of Lie type”, Algebra and Logic, 55:5 (2016), 354–366  mathnet  crossref  crossref  isi
    36. B. Khosravi, A. Babai, “Simple groups with the same prime graph as $D_n(q)$”, Bull. Iran Math. Soc., 42:6 (2016), 1403–1427  mathscinet  zmath  isi
    37. M. F. Ghasemabadi, A. Iranmanesh, “Simple groups with $m$-regular first prime graph component”, Hacet. J. Math. Stat., 45:3 (2016), 705–716  crossref  mathscinet  zmath  isi  scopus
    38. A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010  mathnet  crossref
    39. M. R. Zinoveva, “O konechnykh prostykh lineinykh i unitarnykh gruppakh nad polyami raznykh kharakteristik, grafy prostykh chisel kotorykh sovpadayut. I”, Tr. IMM UrO RAN, 23, no. 4, 2017, 136–151  mathnet  crossref  elib
    40. A. Staroletov, “On almost recognizability by spectrum of simple classical groups”, Int. J. Group Theory, 6:4 (2017), 7–33  crossref  mathscinet  isi
    41. H. Moradi, M. R. Darafsheh, A. Iranmanesh, “Quasirecognition by prime graph of the groups $^2D_{2n}(q)$ where $q < 10^5$”, 6, no. 4, 2018, 57  crossref  isi  scopus
    42. B. Akbari, “ODS-characterization of some low-dimensional finite classical groups”, Int. Electron. J. Algebr., 24 (2018), 73–90  crossref  zmath  isi  scopus
    43. I. B. Gorshkov, N. V. Maslova, “Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups”, Algebra and Logic, 57:2 (2018), 115–129  mathnet  crossref  crossref  isi
    44. M. R. Zinoveva, “O konechnykh prostykh lineinykh i unitarnykh gruppakh malykh razmernostei nad polyami raznykh kharakteristik, grafy prostykh chisel kotorykh sovpadayut”, Tr. IMM UrO RAN, 24, no. 3, 2018, 73–90  mathnet  crossref  elib
    45. Z. Momen, B. Khosravi, “On recognizability of $\operatorname{PSU}_3(q)$ by the orders of maximal abelian subgroups”, Siberian Math. J., 60:1 (2019), 124–139  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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