最高阶元素个数为40的非可解群的分类
Let ψ be a homomorphism from a group Ⅱ to a group Aut(N). Denote by Hψ×N the semidirect product of N by H with homomorphism ψ. This paper proves that: Let G be a finite nonsolvable group. If G has exactly 40 maximal order elements, then G is isomorphic to one of the following groups: (1) Z4ψ×A5,kerψ = Z2; (2) D8ψ× A5, kerψ = Z2×Z2; (3) G/N = S5, N = Z(G) = Z2; (4) G/N = S5, N = Z2 × Z2, N ∩ Z(G) = Z2.
作 者： 杜祥林 刘学飞 王绍恒 DU Xiang Lin LIU Xue Fei WANG Shao Heng 作者单位： School of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing 404000, China 刊 名： 数学研究与评论 ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION 年，卷(期)： 2008 28(3) 分类号： O152.1 关键词： maximal order element non-solvable group simple section