用可解子群的阶的集合刻画有限辛型单群S2n(2m)(n≥3)

journal6 ›› 2008, Vol. 29 ›› Issue (4): 5-10.

用可解子群的阶的集合刻画有限辛型单群S²ⁿ(2^m)(n≥3)

(华南师范大学数学系，广东广州 510631)

出版日期:2008-07-25 发布日期:2012-05-21

A Characterization of Finite Simple Symplectic Groups S²ⁿ(2^m)(n≥3) by Orders of Their Solvable Subgroups

(Department of Mathematics,South-China Normal University,Guangzhou 510631,China)

Online:2008-07-25 Published:2012-05-21
About author:XU Ming-chun (1963-),male,was born in Dazhu County,Sichuan Province,Ph. doctor,associate professor;research area is finite groups theory.
Supported by:
Supported by the National Natural Science Foundation of China (10771077)

摘要/Abstract

摘要：运用有限单群分类定理，证明了有限群Ｇ同构于有限辛型单群S2n(2m)(n≥3)，当且仅当ord(Ssol(G))=ord(Ssol(S2n(2m))),其中ord(Ssol(G))为G的用可解子群的阶的集合.就有限辛型单群S2n(2m)(n≥3)解决了S. Abe和N. Iiyori的一个猜想.

关键词： 有限辛型单群, 可解子群的阶, 单群分类定理, 可解素图

Abstract: In this paper the author has proved the following theorem,which solves a problem of S. Abe and N. Iiyori for finite simple symplectic groups.Let G be a finite group and S2n(2m)(n≥3)　be one of finite simple symplectic groups.Then GS2n(2m) if and only if　ord(Ssol(G))=ord(Ssol(S2n(2m))),where ord(Ssol(G)) is the set of orders of solvable subgroups in G.

Key words: finite simple symplectic groups, orders of solvable subgroups, finite simple groups classification theorem, solvable prime graph

许明春. 用可解子群的阶的集合刻画有限辛型单群S²ⁿ(2^m)(n≥3)[J]. journal6, 2008, 29(4): 5-10.

XU Ming-Chun. A Characterization of Finite Simple Symplectic Groups S²ⁿ(2^m)(n≥3) by Orders of Their Solvable Subgroups[J]. journal6, 2008, 29(4): 5-10.

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用可解子群的阶的集合刻画有限辛型单群S²ⁿ(2^m)(n≥3)

A Characterization of Finite Simple Symplectic Groups S²ⁿ(2^m)(n≥3) by Orders of Their Solvable Subgroups

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