各阶非平凡子群的个数为p+1的p-群的完全分类

各阶非平凡子群的个数为p+1的p-群的完全分类

各阶非平凡子群的个数为p+1的p-群的完全分类 篇1

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)：28(3)分类号：O152.1关键词：maximal order element non-solvable group simple section