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A characterization of the group 2 D n (2), where n=2m+1≥5

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Abstract

In this paper it is proved that the group 2 D n (2), where n=2m+1≥5, can be uniquely determined by its order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G)=OC(2 D n (2)) if and only if G ≅ 2 D n (2). A main consequence of our result is the validity of Thompson’s conjecture for the group under consideration.

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References

  1. Alavi, S.H., Daneshkhah, A.: A new characterization of alternating and symmetric group. J. Appl. Math. Comput. 17(1), 245–258 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen, G.Y.: A new characterization of sporadic simple groups. Algebra Colloq. 3(1), 49–58 (1996)

    MATH  MathSciNet  Google Scholar 

  3. Chen, G.Y.: A new characterization of PSL 2(q). Southeast Asian Bull. Math. 22, 257–263 (1998)

    MATH  MathSciNet  Google Scholar 

  4. Chen, G.Y.: 2 D n (3) (9≤n=2m+1 not a prime) can be characterized by its order components. J. Appl. Math. Comput. 19(1–2), 353–362 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, G.Y.: On Thompson’s conjecture. J. Algebra 185, 184–193 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, G.Y.: On Frobenius and 2-Frobenius groups. J. Southwest China Normal Univ. 20(5), 485–487 (1995)

    Google Scholar 

  7. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Clarendon, Oxford (1985)

    MATH  Google Scholar 

  8. Crescenzo, P.: A diophantine equation which arises in the theory of finite groups. Adv. Math. 17, 25–29 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  9. Darafsheh, M.R., Mahmiani, A.: A quantitative characterization of the linear group L p+1(2). Kumamoto J. Math. 20, 33–50 (2007)

    MATH  MathSciNet  Google Scholar 

  10. Darafsheh, M.R.: Characterizability of the group 2 D p (3) by its order components, where p≥5 is a prime number not of the form 2m+1. Acta Math. Sin. (Engl. Ser.) 24(7), 1117–1126 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Darafsheh, M.R.: On non-isomorphic groups with the same set of order components. J. Korean. Math. Soc. 45, 137–150 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Iranmanesh, A., Alavi, S.H., Khosravi, B.: A characterization of PSL(3,q) where q is an odd prime power. J. Pure. Appl. Algebra 170(2–3), 243–254 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Iranmanesh, A., Alavi, S.H., Khosravi, B.: A characterization of PSL(3,q) for q=2n. Acta Math. Sin. (Engl. Ser.) 18(3), 463–472 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Iranmanesh, A., Khosravi, B., Alavi, S.H.: A characterization of PSU(3,q) for q>5. Southeast Asian Bull. Math. 26(2), 33–44 (2002)

    MATH  MathSciNet  Google Scholar 

  15. Khosravi, A., Khosravi, B.: A new characterization of PSL(p,q). Commun. Algebra 32, 2325–2339 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Khosravi, A., Khosravi, B.: A new characterization of some alternating and symmetric groups. Int. J. Math. Math. Sci. 45, 2863–2872 (2003)

    Article  MathSciNet  Google Scholar 

  17. Khosravi, B., Khosravi, B., Khosravi, B.: The number of isomorphism classes of finite groups with the set of order components of C 4(q). Appl. Algebra Eng. Commun. Comput. 15, 349–359 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Khosravi, A., Khosravi, B.: r-recognizability of B n (q) and C n (q) where n=2m≥4. J. Pure Appl. Algebra 199, 149–165 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. Mazurov, V.D.: Recognition of finite simple groups S 4(q) by their element orders. Algebra Logic 41, 93–110 (2002)

    Article  MathSciNet  Google Scholar 

  20. Shi, H., Chen, G.Y.: 2 D p+1(2) (5<p=2m−1) can be characterized by its order components. Kumamoto J. Math. 18, 1–8 (2005)

    MATH  MathSciNet  Google Scholar 

  21. Williams, J.S.: Prime graph components of finite groups. J. Algebra 69, 487–513 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  22. Zsigmondy, K.: Zur theorie der potenzreste. Mon. Math. Phys. 3, 256–284 (1892)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, College of Science, University of Tehran, Tehran, Iran

    M. R. Darafsheh

  2. Islamic Azad University, Aliabad-e-Katool, Iran

    A. Mahmiani

Authors
  1. M. R. Darafsheh
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  2. A. Mahmiani
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Correspondence to M. R. Darafsheh.

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Darafsheh, M.R., Mahmiani, A. A characterization of the group 2 D n (2), where n=2m+1≥5. J. Appl. Math. Comput. 31, 447–457 (2009). https://doi.org/10.1007/s12190-008-0223-4

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  • DOI: https://doi.org/10.1007/s12190-008-0223-4

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