Geodesic
A Characterization of $PS{{U}_{11}}(q)$
Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 530-539

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2004-052-8
Mots-clés : 20D08, 20D05, 20D60, Prime graph, order component, finite group, simple group 
Iranmanesh, A.; Khosravi, B. A Characterization of $PS{{U}_{11}}(q)$. Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 530-539. doi: 10.4153/CMB-2004-052-8
@article{10_4153_CMB_2004_052_8,
     author = {Iranmanesh, A. and Khosravi, B.},
     title = {A {Characterization} of $PS{{U}_{11}}(q)$},
     journal = {Canadian mathematical bulletin},
     pages = {530--539},
     year = {2004},
     volume = {47},
     number = {4},
     doi = {10.4153/CMB-2004-052-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-052-8/}
}
TY  - JOUR
AU  - Iranmanesh, A.
AU  - Khosravi, B.
TI  - A Characterization of $PS{{U}_{11}}(q)$
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 530
EP  - 539
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-052-8/
DO  - 10.4153/CMB-2004-052-8
ID  - 10_4153_CMB_2004_052_8
ER  - 
%0 Journal Article
%A Iranmanesh, A.
%A Khosravi, B.
%T A Characterization of $PS{{U}_{11}}(q)$
%J Canadian mathematical bulletin
%D 2004
%P 530-539
%V 47
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-052-8/
%R 10.4153/CMB-2004-052-8
%F 10_4153_CMB_2004_052_8

[1] [1] Chen, G. Y., On Frobenius and 2-Frobenius group. J. Southwest China Normal Univ. 20(1995) 485–487. Google Scholar

[2] [2] Chen, G. Y., A new characterization of G2(q), [q ≡ 0(mod3)]. J. Southwest China Normal Univ. (1996), 47–51. Google Scholar

[3] [3] Chen, G. Y., A new characterization of sporadic simple groups. Algebra Colloq. 3 (1996), 49–58. Google Scholar

[4] [4] Chen, G. Y., On Thompson's conjecture. J. Algebra 185 (1996), 184–193. Google Scholar

[5] [5] Chen, G. Y., Further reflections on Thompson's conjecture. J. Algebra 218 (1999), 276–285. Google Scholar

[6] [6] Chen, G. Y., A new characterization of Suzuki-Ree groups. Sci. China (Ser. A) 40 (1997), 807–812. Google Scholar

[7] [7] Chen, G. Y., A new characterization of E8(q). J. Southwest China Normal Univ. 21 (1996), 215–217. Google Scholar

[8] [8] Chen, G. Y., A new characterization of PSL2(q). Southeast Asian Bull. Math, 22 (1998), 257–263. Google Scholar

[9] [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] [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] [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] [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] [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] [14] Iranmanesh, A. and Khosravi, B., A characterization of F(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] [15] Iranmanesh, A. and Khosravi, B., A characterization of C(q) where q > 5. Comment.Math. Univ. Carolin. 43(2002) 9–21. +5.+Comment.Math.+Univ.+Carolin.+43(2002)+9–21.>Google Scholar

[16] [16] Iranmanesh, A. and Khosravi, B., A characterization of PSU(q). Int. Math. J.3 (2003), 129–141. Google Scholar

[17] [17] Iranmanesh, A. and Khosravi, B., A characterization of F(q) where q is an odd prime power. Lecture Note LondonMath. Soc. 304 (2003), 277–283. Google Scholar

[18] [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] [19] Kondrat’ev, A. S., On prime graph components of finite simple groups. Mat. Sb. 180(1989) 787–797. Google Scholar

[20] [20] Shi, W., A new characterization of the sporadic simple groups. In: Group Theory, de Gruyter, Berlin, 1989. Google Scholar

[21] [21] Shi, W., A new characterization of some simple groups of Lie type. Contemp.Math. 82(1989) 171–180. Google Scholar

[22] [22] Shi, W., Pure quantitative characterization of finite simple groups (I)., Prog. Natur. Sci. 4 (1994), 316–326. Google Scholar

[23] [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] [24] Shi, W. and Jianxing, Bi, A new characterization of the alternating groups. Southeast Asian Bull. Math. 17 (1992), 81–90. Google Scholar

[25] [25] Williams, J. S., Prime graph components of finite groups. J. Algebra 69 (1981), 487–513. Google Scholar

Cité par Sources :