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Characterization of G 2(q), where 2 < q ≡ −1(mod 3), by order components

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Abstract

We prove that the simple group G 2(q), where 2 < q ≡ −1(mod 3), is recognizable by the set of its order components. In other words, we prove that if G is a finite group with OC(G) = OC(G 2(q)), then G ≌ G 2(q).

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References

  1. Kondratiev A. S., “Prime graph components of finite simple groups,” Math. USSR-Sb., 67, No. 1, 235–247 (1990).

    Article  MathSciNet  Google Scholar 

  2. Williams J. S., “Prime graph components of finite groups,” J. Algebra, 69, No. 2, 487–513 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  3. Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford (1985).

    MATH  Google Scholar 

  4. Chen G. Y., “A new characterization of PSL2(q),” Southeast Asian Bull. Math., 22, No. 3, 257–263 (1998).

    MathSciNet  MATH  Google Scholar 

  5. Chen G. Y., “Characterization of 3 D 4(q),” Southeast Asian Bull. Math., 25, 389–401 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen G. Y. and Shi H., “2 D n(3) (9 ≤ n = 2m +1 not a prime) can be characterized by its order components,” J. Appl. Math. Comput., 19, No. 1–2, 353–362 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  7. Shi H. and 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).

    MathSciNet  MATH  Google Scholar 

  8. Darafsheh M. R. and Mahmiani A., “A quantitative characterization of the linear groups L p+1(2),” Kumamoto J. Math., 20, 33–50 (2007).

    MathSciNet  MATH  Google Scholar 

  9. 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, No. 7, 1117–1126 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  10. Darafsheh M. R. and Mahmiani A., “A characterization of the group 2 D n(2), where n = 2m + 1 ≥ 5,” J. Appl. Math. Comput., 31, No. 1–2, 447–457 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  11. Darafsheh M. R., “Characterization of the groups D p+1(2) and D p+1(3) using order components,” J. Korean Math. Soc., 47, No. 2, 311–329 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  12. Darafsheh M. R. and Khademi M., “Characterization of the groups D p(q) by order components, where p ≥ 5 is a prime and q = 2, 3 or 5,” Southeast Asian Bull. Math. (to be published).

  13. Iranmanesh A., Alavi S. H., and Khosravi B., “A characterization of PSL(3, q), where q is an odd prime power,” J. Pure Appl. Algebra, 170, No. 2–3, 243–254 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  14. Iranmanesh A., Alavi S. H., and Khosravi B., “A characterization of PSL(3, q) for q = 2n,” Acta Math. Sin. (Engl. Ser.), 18, No. 3, 463–472 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  15. Iranmanesh A., Khosravi B., and Alavi S. H., “A characterization of PSU(3, q) for q > 5,” South Asian Bull. Math., 26, No. 2, 33–44 (2002).

    MathSciNet  MATH  Google Scholar 

  16. Khosravi Behrooz and Khosravi Bahnam, “A characterization of E 6(q),” Algebras, Groups Geom., 19, 225–243 (2002).

    MathSciNet  MATH  Google Scholar 

  17. Khosravi Behrooz and Khosravi Bahnam, “A characterization of 2 E 6(q),” Kumamoto J. Math., 16, 1–11 (2003).

    MathSciNet  MATH  Google Scholar 

  18. Khosravi A. and Khosravi B., “A characterization of 2 D n(q), where n = 2m,” Internat. J. Math. Game Theory and Algebra, 13, 253–265 (2003).

    MathSciNet  MATH  Google Scholar 

  19. Khosravi A. and Khosravi B., “A new characterization of PSL(p, q),” Comm. Algebra, 32, 2325–2339 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  20. Khosravi Bahman, Khosravi Behnam, and Khosravi B., “A new characterization of PSU(p, q),” Acta Math. Hungar., 107, No. 3, 235–252 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  21. Khosravi Behrooz, Khosravi Bahman, and Khosravi Behnam, “Characterizability of PSL(p + 1, q) by its order components,” Houston J. Math., 32, No. 3, 683–700 (2006).

    MathSciNet  MATH  Google Scholar 

  22. Khosravi A. and Khosravi B., “Characterizability of PSU(p + 1, q) by its order components,” Rocky Mount. J. Math., 36, No. 5, 1555–1575 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  23. Khosravi A. and 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  MathSciNet  MATH  Google Scholar 

  24. Khademi M., “Characterizability of finite simple groups by their order components: a summary of results,” Int. J. Algebra, 4, No. 9, 413–420 (2010).

    MathSciNet  MATH  Google Scholar 

  25. Chen G. Y., “A new characterization of sporadic simple groups,” Algebra Colloq., 3, No. 1, 49–58 (1996).

    MathSciNet  MATH  Google Scholar 

  26. Chen G. Y., “On Frobenius and 2-Frobenius group,” J. Southwest China Normal Univ., 20, No. 5, 485–487 (1995).

    Google Scholar 

  27. Zsigmondy K., “Zür Theorie der Potenzreste,” Monatsh. Math. Phys., 3, No. 1, 265–284 (1892).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran

    P. Nosratpour

  2. School of Mathematics, Statistics and Computer Sciences College of Science, University of Tehran, Tehran, Iran

    M. R. Darafsheh

Authors
  1. P. Nosratpour
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  2. M. R. Darafsheh
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Correspondence to P. Nosratpour.

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Original Russian Text Copyright © 2013 Nosratpour P. and Darafsheh M.R.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 5, pp. 1102–1114, September–October, 2013.

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Nosratpour, P., Darafsheh, M.R. Characterization of G 2(q), where 2 < q ≡ −1(mod 3), by order components. Sib Math J 54, 883–893 (2013). https://doi.org/10.1134/S0037446613050121

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  • DOI: https://doi.org/10.1134/S0037446613050121

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