摘要
用μ（G）表群G的极大子群共轭类的代表系。设1=G<sub>0</sub>【G<sub>1</sub>【…【G<sub>（?）+1</sub><sup>m</sup>=G是G的主群列,如果G<sub>1</sub>/G<sub>i-1</sub>,■φ(G/G<sub>i-1</sub>,那么我们就称G<sub>1</sub>/G<sub>i-1</sub>为G的生成主因子。本文从主群列的角度部分地解决了施武杰教授在中国数学会1987年有限群学术交流会上提出的一个问题。证明了定理设G是有限可解群,那么|π（G）|=|μ（G）|当且仅当G的每个生成主因子N<sub>i+1</sub><sup>m</sup>/N<sub>1</sub>是G/N<sub>1</sub>的Sylow子群。
Let μ(G) denote the set of conjugacy classes representative of maximal subgroup of group G. Let 1=G_0<G_1<G_2<…<G_r<G_(r+1)=G be a chief Series of G, G_1/G_(i-1) is said to be a generating principal factor of G, if G_i/G_(i-1)■ (G/G_(i-1)) .In this paper, We discussed the problem that Professor Shi Wujie raised on China Mathematical Society Annual Confe- rence On Finite Groups in 1987 and proved the following theorem: Theorem Let G be a finite solvable group, then |μ(G)|=|π(G)|if and only if every generating Chief factor N_(i+1)/N_i of G is Sylow Subgroup of G/N_1.
出处
《贵州师范大学学报（自然科学版）》
CAS
1992年第2期38-41,共4页
Journal of Guizhou Normal University：Natural Sciences
基金
贵州省自然科学基金
关键词
可解群
极大子群
共轭类
因子群
Solvable Groups
Maximal Subgroup
Conjugacy Classes
Factor Group
