用可解子群的阶刻画有限单群被引量：2

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摘要设G是有限群,S是有限单群．在这篇文章中,我们证明:如果G和S的可解子群的阶集合相同,那么G与S同构,或G和S同构于Bn(Q)和Cn(q),其中q是奇数,n≥3．

作者 K.Denecke 黎先华毕建行

机构地区 Institut für Mathematik Universitt Potsdam 苏州大学数学科学学院辽宁大学数学系

出处《中国科学（A辑）》 CSCD 北大核心 2007年第2期189-199,共11页 Science in China(Series A)

基金国家自然科学基金(批准号:10571128) 苏州市高层次人才资助项目

关键词有限单群可解子群阶刻画

参考文献22

1Thompson J G. Nonsolvable finite groups all of whose local subgroups are solvable I. Bull Amer Math Soc,1986, 74:383-437
2Mazurov V D, Sitnikov V M, Syskin S A. Finite groups whose solvable subgroup are 2-closed or 2'-closed.Algebra I Logika, 1979, 9:313-341
3Li S R, Zhao Y Q. Some finite nonsolvable groups characterized by their solvable subgroups. Acta Math Sinica, New Series, 1988, 4(1): 5-13
4Li X H, Wang D J. Some finite nonsolvable groups characterized by teir solvable subgroups. Communications in Algebra, 1996, 24(7): 2221-2233
5Abe S. A characterization of some finitr simple groups by orders of their solvable subgroups. Hokkaido Mathematical Journal, 2002, 31:349-361
6Kimmerle W, Lyons R, Sanding R, et al. Composition factors from the group ring and Artin's theorem on orders of simple groups. Proc London Math Soc, 1990, 60(3): 89-122
7Aschbacher M, Seitz G N. Involutions in chevalley groups over field of even order. Nagoya Math J, 1976,63:1-91
8Cohen A M, Liebeck M W, Saxl J, et al. The local maximal subgroups of exceptional groups of Lie type,finite and Algebraic. Proc London Math Soc, 1992, 64(3): 21-48
9Liebeck M W, Praeger C E, Saxl J. Transitive subgroups of primitive permutation groups. Journal of Algebra, 2000, 234:291-361
10Liebeck M W, Saxl J, Seitz G M. Subgroups of maximal rank in exceptional groups of Lie type. Proc London Math Soc, 1992, 65(3): 297-325

1王殿军.用极大子群阶之集刻划有限单群[J].西南师范大学学报（自然科学版）,1993,18(1):18-21. 被引量：8
2陈重穆,施武杰.关于C_(pp)单群[J].西南师范大学学报（自然科学版）,1993,18(3):249-256. 被引量：16
3施武杰.关于有限单群的阶.科学通报,1993,38(4):296-298.
4Li X H, A characterization of Finite Simple Group [ J ]. Journal of Algebra,2001,245:620-649.
5H. Kurzweil, B. Stellmacher. The Theory of Finite Groups [ M ]. New York: Springer-verlag,2004.
6徐明曜.有限群导引(上册)[M].北京:科学出版社,1982.
7ROBERT A. The finite simple groups[M]. New York: Springer Berlin, 2007.
8KURZWEIL H, STELLMACHCR B. The thery of finite groups[M]. New York: Springerverlay, 2004.
9KLEIDMAN P, LIEBCK M. The subgroup structure of the finite classical groups[M]. UK; Cambridge Univ Press, 1998.
10徐明耀．有限群导引(下册)[M]．北京：科学出版社．2001．

中国科学（A辑）

2007年第2期

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