General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Algebra Logika:

Personal entry:
Save password
Forgotten password?

Algebra Logika, 2002, Volume 41, Number 2, Pages 166–198 (Mi al179)  

This article is cited in 64 scientific papers (total in 64 papers)

Recognition of Finite Simple Groups $S_4(q)$ by Their Element Orders

V. D. Mazurov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: It is proved that among simple groups $S_4(q)$ in the class of finite groups, only the groups $S_4(3^n)$, where $n$ is an odd number greater than unity, are recognizable by a set of their element orders. It is also shown that simple groups $U_3(9)$, ${^3D}_4(2)$, $G_2(4)$, $S_6(3)$, $F_4(2)$, and ${^2E}_6(2)$ are recognizable, but $L_3(3)$ is not.

Keywords: finite simple groups, recognizability of groups by their element orders

Full text: PDF file (2630 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2002, 41:2, 93–110

Bibliographic databases:

UDC: 512.542
Received: 29.11.2000

Citation: V. D. Mazurov, “Recognition of Finite Simple Groups $S_4(q)$ by Their Element Orders”, Algebra Logika, 41:2 (2002), 166–198; Algebra and Logic, 41:2 (2002), 93–110

Citation in format AMSBIB
\by V.~D.~Mazurov
\paper Recognition of Finite Simple Groups~$S_4(q)$ by Their Element Orders
\jour Algebra Logika
\yr 2002
\vol 41
\issue 2
\pages 166--198
\jour Algebra and Logic
\yr 2002
\vol 41
\issue 2
\pages 93--110

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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:
    1. O. A. Alekseeva, A. S. Kondrat'ev, “Quasirecognition of one class of finite simple groups by the set of element orders”, Siberian Math. J., 44:2 (2003), 195–207  mathnet  crossref  mathscinet  zmath  isi
    2. M. A. Grechkoseeva, “Recognition of the group $O_{10}^+(2)$ from its spectrum”, Siberian Math. J., 44:4 (2003), 577–580  mathnet  crossref  mathscinet  zmath  isi
    3. M. R. Aleeva, “On Finite Simple Groups with the Set of Element Orders as in a Frobenius Group or a Double Frobenius Group”, Math. Notes, 73:3 (2003), 299–313  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. V. Zavarnitsin, “The weights of irreducible $SL_3(q)$-modules in the defining characteristic”, Siberian Math. J., 45:2 (2004), 261–268  mathnet  crossref  mathscinet  zmath  isi
    5. 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”, Siberian Math. J., 45:3 (2004), 420–432  mathnet  crossref  mathscinet  zmath  isi
    6. A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, Kh. P. Chao, G. Yu. Chen, W. Shi, “Recognition of the finite simple groups $F_4(2^m)$ by spectrum”, Siberian Math. J., 45:6 (2004), 1031–1035  mathnet  crossref  mathscinet  zmath  isi  elib
    7. Moghaddamfar AR, Darafsheh MR, “A family of finite simple groups which are 2-recognizable by their elements order”, Communications in Algebra, 32:11 (2004), 4507–4513  crossref  mathscinet  zmath  isi  scopus
    8. Lucido MS, Moghaddamfar AR, “Groups with complete prime graph connected components”, Journal of Group Theory, 7:3 (2004), 373–384  crossref  mathscinet  zmath  isi  scopus
    9. Zavarnitsine AV, “Recognition of the simple groups L-3(q) by element orders”, Journal of Group Theory, 7:1 (2004), 81–97  crossref  mathscinet  zmath  isi
    10. Darafsheh MR, Moghaddamfar AR, Zokayi AR, “A recognition of simple groups PSL(3,q) by their element orders”, Acta Mathematica Scientia, 24:1 (2004), 45–51  crossref  mathscinet  zmath  isi
    11. Mazurov VD, “Characterizations of groups by arithmetic properties”, Algebra Colloquium, 11:1 (2004), 129–140  mathscinet  zmath  isi
    12. A. R. Moghaddamfar, W. Shi, W. Zhou, A. R. Zokayi, “On the noncommuting graph associated with a finite group”, Siberian Math. J., 46:2 (2005), 325–332  mathnet  crossref  mathscinet  zmath  isi
    13. 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
    14. O. A. Alekseeva, A. S. Kondrat'ev, “Quasirecognizability by the Set of Element Orders for Groups $^3D_4(q)$ and $F_4(q)$, for $q$ Odd”, Algebra and Logic, 44:5 (2005), 287–301  mathnet  crossref  mathscinet  zmath  elib
    15. V. I. Senashov, A. I. Sozutov, V. P. Shunkov, “Investigation of groups with finiteness conditions in Krasnoyarsk”, Russian Math. Surveys, 60:5 (2005), 805–848  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Xu M.C., “The characterization of finite simple groups, L-3(3(2m-1))(m >= 2), by their element orders”, Acta Mathematica Sinica-English Series, 21:4 (2005), 899–902  crossref  mathscinet  zmath  isi  scopus
    17. M. A. Grechkoseeva, M. S. Lucido, V. D. Mazurov, A. R. Moghaddamfar, A. V. Vasil'ev, “On recognition of the projective special linear groups over binary fields”, Sib. elektron. matem. izv., 2 (2005), 253–263  mathnet  mathscinet  zmath
    18. 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
    19. A. V. Zavarnitsin, “Recognition of Simple Groups $U_3(Q)$ by Element Orders”, Algebra and Logic, 45:2 (2006), 106–116  mathnet  crossref  mathscinet  zmath
    20. A. V. Zavarnitsin, “Recognition of Finite Groups by the Prime Graph”, Algebra and Logic, 45:4 (2006), 220–231  mathnet  crossref  mathscinet  zmath  elib  elib
    21. M. S. Lucido, A. R. Moghaddamfar, “Recognition by spectrum of some linear groups over the binary field”, Siberian Math. J., 47:1 (2006), 86–96  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    22. Abdollahi A., Hassanabadi A.M., “Noncyclic graph of a group”, Communications in Algebra, 35:7 (2007), 2057–2081  crossref  mathscinet  zmath  isi  scopus
    23. Chen G.Y., Mazurov V.D., Shi W.J., Vasil'ev A.V., Zhurtov A.Kh., “Recognition of the finite almost simple groups PGL(2)(q) by their spectrum”, Journal of Group Theory, 10:1 (2007), 71–85  crossref  mathscinet  zmath  isi  scopus
    24. V. D. Mazurov, G. Y. Chen, “Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum”, Algebra and Logic, 47:1 (2008), 49–55  mathnet  crossref  mathscinet  zmath  isi
    25. M. R. Darafsheh, A. Sadrudini, “A characterization of the simple group $PSL_5(5)$ by the set of its element orders”, Siberian Math. J., 49:3 (2008), 418–422  mathnet  crossref  mathscinet  zmath  isi  elib
    26. Khukhro E.I., “Graded Lie rings with many commuting components and an application to 2-Frobenius groups”, Bulletin of the London Mathematical Society, 40:5 (2008), 907–912  crossref  mathscinet  zmath  isi  scopus
    27. Darafsheh M.R., “On the recognition of the simple groups L-7(3) and L-8(3) by the spectrum”, International Journal of Algebra and Computation, 18:5 (2008), 925–933  crossref  mathscinet  zmath  isi  scopus
    28. Darafsheh M.R., Karamzadeh N.S., “On recognition property of some projective special linear groups by their element orders”, Utilitas Mathematica, 75 (2008), 125–137  mathscinet  zmath  isi  elib
    29. 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
    30. 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  mathnet  crossref  mathscinet  isi  elib  elib
    31. 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  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    32. Ahanjideh N., Iranmanesh A., “A Characterization of Bn(q) by the Set of Orders of Maximal Abelian Subgroups”, International Journal of Algebra and Computation, 19:2 (2009), 191–211  crossref  mathscinet  zmath  isi  scopus
    33. E. I. Khukhro, “Koltsa Li s konechnoi tsiklicheskoi graduirovkoi, v kotoroi mnogo kommutiruyuschikh komponent”, Sib. elektron. matem. izv., 6 (2009), 243–250  mathnet  mathscinet  elib
    34. A. V. Zavarnitsine, “A solvable group isospectral to $\mathrm S_4(3)$”, Siberian Math. J., 51:1 (2010), 20–24  mathnet  crossref  mathscinet  isi
    35. Vasil'ev A.V., Grechkoseeva M.A., Mazurov V.D., “Recognizability of the finite simple groups by spectrum and order”, Doklady Mathematics, 81:2 (2010), 216–218  crossref  mathscinet  zmath  isi  scopus
    36. Darafsheh M.R., “Recognition of the projective special linear group over GF(3)”, Acta Mathematica Sinica-English Series, 26:3 (2010), 477–488  crossref  mathscinet  zmath  isi  scopus
    37. M. R. Zinoveva, “Raspoznavanie po spektru prostykh grupp $C_p(3)$”, Tr. IMM UrO RAN, 16, no. 3, 2010, 88–95  mathnet  elib
    38. Akhlaghi Z., Khosravi B., Khatami M., “Characterization by prime graph of PGL(2, p(k)) where p and k > 1 are odd”, International Journal of Algebra and Computation, 20:7 (2010), 847–873  crossref  mathscinet  zmath  isi  scopus
    39. Makarenko N.Yu., Shumyatsky P., “Frobenius Groups as Groups of Automorphisms”, Proceedings of the American Mathematical Society, 138:10 (2010), 3425–3436  crossref  mathscinet  zmath  isi  scopus
    40. V. D. Mazurov, “Periodic groups with prescribed element orders”, Tr. In-ta matem., 18:1 (2010), 72–78  mathnet
    41. A. V. Vasil'ev, M. A. Grechkoseeva, A. M. Staroletov, “On finite groups isospectral to simple linear and unitary groups”, Siberian Math. J., 52:1 (2011), 30–40  mathnet  crossref  mathscinet  isi
    42. Khatami M., Khosravi B., Akhlaghi Z., “NCF-Distinguishablity by prime graph of PGL (2, p) where p is a prime”, Rocky Mountain J Math, 41:5 (2011), 1523–1545  crossref  mathscinet  zmath  isi  elib  scopus
    43. A. M. Staroletov, “Sporadic composition factors of finite groups isospectral to simple groups”, Sib. elektron. matem. izv., 8 (2011), 268–272  mathnet
    44. A. M. Staroletov, “On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$”, Siberian Math. J., 53:3 (2012), 532–538  mathnet  crossref  mathscinet  isi
    45. 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
    46. Nosratpour P., Darafsheh M.R., “Recognition of the Groups l (5)(4) and U (4)(4) by the Prime Graph”, Ukr. Math. J., 64:2 (2012), 238–246  crossref  mathscinet  zmath  isi  elib  scopus
    47. A. V. Vasil'ev, A. M. Staroletov, “Recognizability of groups $G_2(q)$ by spectrum”, Algebra and Logic, 52:1 (2013), 1–14  mathnet  crossref  mathscinet  zmath  isi
    48. Yu. V. Lytkin, “On groups critical with respect to a set of natural numbers”, Sib. elektron. matem. izv., 10 (2013), 666–675  mathnet
    49. V. D. Mazurov, “Unrecognizability by spectrum for a finite simple group $^3D_4(2)$”, Algebra and Logic, 52:5 (2013), 400–403  mathnet  crossref  mathscinet  isi
    50. A. S. Kondrat'ev, “Recognizability of groups $E_7(2)$ and $E_7(3)$ by prime graph”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 139–145  mathnet  crossref  mathscinet  isi  elib
    51. D. V. Lytkina, V. D. Mazurov, A. S. Mamontov, E. Jabara, “Groups whose element orders do not exceed 6”, Algebra and Logic, 53:5 (2014), 365–376  mathnet  crossref  mathscinet  isi
    52. V. D. Mazurov, “Neraspoznavaemye po spektru konechnye prostye gruppy i izospektralnye im gruppy”, Vladikavk. matem. zhurn., 17:2 (2015), 47–55  mathnet
    53. V. D. Mazurov, “$2$-Frobenius groups isospectral to the simple group $U_3(3)$”, Siberian Math. J., 56:6 (2015), 1108–1113  mathnet  crossref  crossref  mathscinet  isi  elib
    54. 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  crossref  mathscinet  zmath  isi  elib  scopus
    55. Vasil'ev A.V., “on Finite Groups Isospectral To Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    56. Akbari B. Moghaddamfar A.R., “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
    57. Moghaddamfar A.R. Rahbariyan S., “Od-Characterization of Some Projective Special Linear Groups Over the Binary Field and Their Automorphism Groups”, Commun. Algebr., 43:6 (2015), 2308–2334  crossref  mathscinet  zmath  isi  elib  scopus
    58. 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
    59. Akbari B., Iiyori N., Moghaddamfar A.R., “a New Characterization of Some Simple Groups By Order and Degree Pattern of Solvable Graph”, Hokkaido Math. J., 45:3 (2016), 337–363  crossref  mathscinet  zmath  isi  scopus
    60. Nosratpour P. Darafsheh M.R., “Characterization of the Group G(2)(5) By the Prime Graph”, Ukr. Math. J., 68:8 (2017), 1308–1313  crossref  mathscinet  isi  scopus
    61. Mohammadzadeh A. Moghaddamfar A.R., “Several Quantitative Characterizations of Some Specific Groups”, Comment. Math. Univ. Carol., 58:1 (2017), 19–34  crossref  mathscinet  zmath  isi  scopus
    62. W. Guo, A. S. Mamontov, “On groups whose element orders divide $6$ and $7$”, Siberian Math. J., 58:1 (2017), 67–71  mathnet  crossref  crossref  isi  elib  elib
    63. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    64. 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
    Number of views:
    This page:548
    Full text:213
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019