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A Characterization of $PS{{U}_{11}}(q)$

Published online by Cambridge University Press:  20 November 2018

A. Iranmanesh  and
B. Khosravi
A. Iranmanesh
Affiliation:
Department of Mathematics Tarbiat Modarres University P. O. Box: 14115-137 Tehran Iran and Institute for Studies in Theoretical Physics and Mathematics Tehran Iran e-mail: [email protected]
B. Khosravi
Affiliation:
Department of Mathematics Tarbiat Modarres University P. O. Box: 14115-175 Tehran Iran
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Abstract

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Order components of a finite simple group were introduced in [4]. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper, we show that groups $PS{{U}_{11}}(q)$ are also uniquely determined by their order components. As corollaries of this result, the validity of a conjecture of J. G. Thompson and a conjecture of W. Shi and J. Bi both on $PS{{U}_{11}}(q)$ are obtained.

Keywords

20D0820D0520D60Prime graphorder componentfinite groupsimple group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 4 , 01 December 2004 , pp. 530 - 539
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Chen, G. Y., On Frobenius and 2-Frobenius group. J. Southwest China Normal Univ. 20(1995) 485–487.Google Scholar
[2] Chen, G. Y., A new characterization of G2(q), [q ≡ 0(mod3)]. J. Southwest China Normal Univ. (1996), 47–51.Google Scholar
[3] Chen, G. Y., A new characterization of sporadic simple groups. Algebra Colloq. 3 (1996), 49–58.Google Scholar
[4] Chen, G. Y., On Thompson's conjecture. J. Algebra 185 (1996), 184–193.Google Scholar
[5] Chen, G. Y., Further reflections on Thompson's conjecture. J. Algebra 218 (1999), 276–285.Google Scholar
[6] Chen, G. Y., A new characterization of Suzuki-Ree groups. Sci. China (Ser. A) 40 (1997), 807–812.Google Scholar
[7] Chen, G. Y., A new characterization of E8(q). J. Southwest China Normal Univ. 21 (1996), 215–217.Google Scholar
[8] Chen, G. Y., A new characterization of PSL2(q). Southeast Asian Bull. Math, 22 (1998), 257–263.Google Scholar
[9] Gruenberg, K. W. and Roggenkamp, K. W., Decomposition of the augmentation ideal and of the relation modules of a finite group. Proc. LondonMath. Soc. 31(1975) 149–166.Google Scholar
[10] Iranmanesh, A. and Alavi, S. H., A new characterization of Ap where p and p - 2 are primes. Korean J. Comput. Appl. Math. 8 (2001), 665–673.Google Scholar
[11] Iranmanesh, A. and Alavi, S. H., A characterization of simple groups PSL (5, q). Bull. Austral.Math. Soc. 65 (2002) 211–222.Google Scholar
[12] 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 (2002), 243–254.Google Scholar
[13] Iranmanesh, A., Alavi, S. H. and Khosravi, B., A characterization of PSL (3, q) for q = 2m . Acta Math. Sinica 18 (2002), 463–472.Google Scholar
[14] Iranmanesh, A. and Khosravi, B., A characterization of F4(q) where q = 2n(n > 1). Far East J. Math. Sci. 2(2000) 853–859.+1).+Far+East+J.+Math.+Sci.+2(2000)+853–859.>Google Scholar
[15] Iranmanesh, A. and Khosravi, B., A characterization of C2(q) where q > 5. Comment.Math. Univ. Carolin. 43(2002) 9–21.+5.+Comment.Math.+Univ.+Carolin.+43(2002)+9–21.>Google Scholar
[16] Iranmanesh, A. and Khosravi, B., A characterization of PSU5(q). Int. Math. J.3 (2003), 129–141.Google Scholar
[17] Iranmanesh, A. and Khosravi, B., A characterization of F4(q) where q is an odd prime power. Lecture Note LondonMath. Soc. 304 (2003), 277–283.Google Scholar
[18] Iranmanesh, A., Khosravi, B. and Alavi, S. H., A characterization of PSU(3, q) for q > 5. Southeast Asian Bull. Math. 26(2002) 33–44.+5.+Southeast+Asian+Bull.+Math.+26(2002)+33–44.>Google Scholar
[19] Kondrat’ev, A. S., On prime graph components of finite simple groups. Mat. Sb. 180(1989) 787–797.Google Scholar
[20] Shi, W., A new characterization of the sporadic simple groups. In: Group Theory, de Gruyter, Berlin, 1989.Google Scholar
[21] Shi, W., A new characterization of some simple groups of Lie type. Contemp.Math. 82(1989) 171–180.Google Scholar
[22] Shi, W., Pure quantitative characterization of finite simple groups (I)., Prog. Natur. Sci. 4 (1994), 316–326.Google Scholar
[23] Shi, W. and Jianxing, Bi, A characteristic property for each finite projective special linear group. Lecture Notes in Math. 1456 (1990), 171–180.Google Scholar
[24] Shi, W. and Jianxing, Bi, A new characterization of the alternating groups. Southeast Asian Bull. Math. 17 (1992), 81–90.Google Scholar
[25] Williams, J. S., Prime graph components of finite groups. J. Algebra 69 (1981), 487–513.Google Scholar