The Number of Isomorphism Classes of Finite Groups with the set of Order Components of C 4 (q) (original) (raw)

Abstract.

Let G be a finite group. Based on the prime graph of G, the order of G can be divided into a product of coprime positive integers. These integers are called order components of G and the set of order components is denoted by OC(G). Some non-abelian simple groups are known to be uniquely determined by their order components.

In this paper we prove that if q_=2_n, then the simple group _C_4(q) can be uniquely determined by its order components. Also if q is an odd prime power and OC(G)=OC(_C_4(q)), then _G_≅_C_4(q) or _G_≅_B_4(q).

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References

  1. Blackburn, N., Huppert, B.: Finite Groups III. Springer, Berlin, 1982
  2. Chen, G.Y.: On Frobenius and 2-Frobenius group. J. Southwest China Normal Univ. 20(5), 485–487 (1995)
    Google Scholar
  3. Chen, G.Y.: A new characterization of _G_2(q), [q≡ 0 ( mod 3)]. J. Southwest China Normal Univ. pp. 47–51, 1996
  4. Chen, G.Y.: A new characterization of sporadic simple groups. Algebra Colloq. 3(1), 49–58 (1996)
    Google Scholar
  5. Chen, G.Y.: On Thompson’s conjecture. J. Algebra 185, 184–193 (1996)
    Article MATH Google Scholar
  6. Chen, G.Y.: Further reflections on Thompson’s conjecture. J. Algebra 218, 276–285 (1999)
    Article MATH Google Scholar
  7. Chen, G.Y.: A new characterization of Suzuki-Ree groups. Sci. in China(ser A) 27(5), 430–433 (1997)
    MATH Google Scholar
  8. Chen, G.Y.: A new characterization of _E_8(q). J. Southwest China Normal Univ. 21(3), 215–217 (1996)
    Google Scholar
  9. Chen, G.Y.: A new characterization of _PSL_2(q). Southeast Asian Bulletin of Math. 22, 257–263 (1998)
    Google Scholar
  10. Conway, J., Curtis, R., Norton, S., Parker, R., Wilson, R.: Atlas of finite groups. Clarendon press, Oxford, 1985
  11. Gorenstien, D.: Finite groups. Harper and Row, New York, 1968
  12. Gruenberg, K.W., Roggenkamp, K.W.: Decomposition of the augmentation ideal and of the relation modules of a finite group. Proc. London Math. Soc. 31, 146–166 (1975)
    Google Scholar
  13. Iranmanesh, A., Alavi, S.H., Khosravi, B.: A Characterization of PSL(3,q) where q is an odd prime power. J. Pure and Applied Algebra 170(2–3), 243–254 (2002)
  14. Iranmanesh, A., Alavi, S.H., Khosravi, B.: A Characterization of PSL(3,q) where q_=2_n. Acta Math. Sinica, English Series 18(3), 463–472 (2002)
    Google Scholar
  15. Iranmanesh, A., Khosravi, B., Alavi, S.H.: A Characterization of PSU(3,q) where _q_>5. Southeast Asian Bull. Math. 26(2), 33–44 (2002)
    MATH Google Scholar
  16. Iranmanesh, A., Khosravi, B.: A characterization of _F_4(q) where q_=2_n (_n_>1). Far East Journal of Mathematical Sciences 6(2), 853–859 (2000)
    MATH Google Scholar
  17. Iranmanesh, A., Khosravi, B.: A characterization of _C_2(q) where _q_>5. Comment. Math. Univ. Carolinae 43(1), 9–21 (2002)
    Google Scholar
  18. Khosravi, A., Khosravi, B.: A new characterization of almost sporadic simple groups. J. Algebra and its Applications. 1(3), 267–279 (2002)
    Article MATH Google Scholar
  19. Khosravi, A., Khosravi, B.: A new characterization of PSL(p,q). Commun. Algebra 32(6), 2325–2339 (2004)
    Article Google Scholar
  20. Behrooz khosravi, Behnam Khosravi: A characterization of _E_6(q). Algebras, Groups and Geometries 19(2), 225–243 (2002)
    Google Scholar
  21. Behrooz khosravi, Bahman Khosravi: A characterization of 2_E_6(q). Kumamoto journal of Math. 16, 1–11 (2003)
    Google Scholar
  22. Kondtrat’ev, A.S.: Prime graph components of finite groups. Math. USSR-sb. 67(1), 235–247 (1990)
    Google Scholar
  23. Williams, J.S.: Prime graph components of finite groups. J. Algebra 69, 487–513 (1981)
    MATH Google Scholar

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Authors and Affiliations

  1. Department of Pure Math., Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran
    Behrooz Khosravi
  2. Institute for Studies in Theoretical Physics and Mathematics (IPM),
    Behrooz Khosravi
  3. Dept. Math., Faculty Math. Sci., Shahid Beheshti Univ., Evin, Tehran, 19838, Iran
    Behnam Khosravi & Bahman Khosravi

Authors

  1. Behrooz Khosravi
  2. Behnam Khosravi
  3. Bahman Khosravi

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Correspondence toBehrooz Khosravi.

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The first author was supported in part by a grant from IPM (No. 82200031).

Acknowledgement The authors express their gratitude to professor Calmet and the referees for carefully reading and several valuable pointers which improved the manuscript. The first author would like to thank the Institute for Studies in Theoretical Physics and Mathematics (IPM) for the financial support. We dedicate this paper to our parents: Professor Amir Khosravi and Mrs. Soraya Khosravi for their unending love and supports.

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Khosravi, B., Khosravi, B. & Khosravi, B. The Number of Isomorphism Classes of Finite Groups with the set of Order Components of C 4 (q).AAECC 15, 349–359 (2005). https://doi.org/10.1007/s00200-004-0166-4

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