单群G2(3n)的拟刻画

李立莉

数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 257-262.

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数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 257-262. DOI: 10.12386/A2013sxxb0027
论文

单群G2(3n)的拟刻画

    李立莉
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Quasirecognition of the Simple Group G2(3n)

    Li Li LI
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摘要

设G为有限群, 且满足M(G)=M(G2(3n)),其中n≥1,则G必有正规子群同构于G2(3n). 特别地, 若|G|=|G2(3n)|,则G≌G2(3n).

Abstract

Let G be finite group such that M(G)=M(G2(3n)), where n≥1. Then G has a normal subgroup isomorphic to G2(3n). Especially, if |G|=|G2(3n)|, then G≌G2(3n).

关键词

单群 / 极大交换子群 / 阶分量

Key words

simple group / maximal abelian subgroup / order component

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李立莉. 单群G2(3n)的拟刻画. 数学学报, 2013, 56(2): 257-262 https://doi.org/10.12386/A2013sxxb0027
Li Li LI. Quasirecognition of the Simple Group G2(3n). Acta Mathematica Sinica, Chinese Series, 2013, 56(2): 257-262 https://doi.org/10.12386/A2013sxxb0027

参考文献

[1] Shi W. J., A New Characterization of the Sporadic Simple Groups, Group Theory Porc. Singapore Group Theory Conf. 1987, Walter de Gruyter, Berlin, New York, 1989.

[2] Shi W. J., Bi J. X., A characteristic property for each finite projective special linear group, Lecture Notes in Math., Springer-Verlag, 1990, 1456: 171-180.

[3] Shi W. J., Bi J. X., A characterization of Suzuki-Ree groups, Sci. China, Ser. A, 1991, 34 (1): 14-19.

[4] Shi W. J., Bi J. X., A new characterization of the alternating groups, Southeast Asian Bull. Math., 1992, 17(1): 81-90.

[5] Shi W. J., The pure quantitative characterization of finite simple groups (I), Prog. Nat. Sci., 1994, 4: 316- 326.

[6] Cao H. P., Shi W. J., Pure quantitative characterization of finite projective special unitary groups, Sci. China, Ser. A, 2002, 45: 761-772.

[7] Vasil'ev A. V., Grechkoseeva M. A., Mazurov V. D., Characterization of the finite simple groups by spectrum and order, Algebra and Logic, 2002, 48(6): 385-409.

[8] Xu M. C., Shi W. J., Pure quantitative characterization of finite simple groups 2Dn(q) and Dl(q) (l odd), Alg. Coll., 2003, 10(3): 427-443.

[9] Shi W. J., Pure quantitative characterization of finite simple groups, Front. Math. China., 2007, 2(1): 123- 125.

[10] Grechkoseeva M. A., On difference between the spectra of the simple groups Bn(q) and Cn(q), Siberian Math. J., 2007, 48(1): 73-75.

[11] Vasilev A. V., Grechkoseeva M. A., Mazurov V. D., On finite groups isospectral to simple symplectic and orthogonal groups, Siberian Math. J., 2009, 50(6): 965-981.

[12] Wang L. H., Characterization of Some Classes of Finite Simple Groups (in Chinese), Thesis for Master of Science, Southwest Normal University, Chongqing, 2000.

[13] Chen G. Y., A new characterization of sporadic simple groups, Algebra Colloquium, 1996, 3(1): 49-58.

[14] Crescenzo P., A diophantine equation which arises in the theory of finite groups, Adv. Math., 1975, 17: 25-29.

[15] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., Atlas of Finite Groups, Oxford University Press, Oxford, Clarendon, 1985.

基金

湛江师范学院博士专项基金资助项目(ZL1108);重庆市科委资助项目(KJ110609)

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