子群的半覆盖—避开性与有限群的结构  

Semi CAP-Subgroups and the Structure of Finite Groups

作　　者：黎先华[1] 杨元韡[1] 

机构地区：[1]苏州大学数学科学学院,苏州215006

出　　处：《数学学报（中文版）》2008年第6期1181-1186,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10571128);苏州市高层次人才项目资助项目

摘　　要：设G是有限群,H为G的子群.如果存在一个主群列1=G_0(?)G_1(?)…(?) G_(n-1)(?)G_n=G,使得对每个i=1,2,…,n,或者H覆盖G_i/G_(i-1),或者H避开G_i/G_(i-1),则称H为G的半覆盖—避开子群.利用G的Sylow子群的极大子群,Sylow子群的2-极大子群的半覆盖—避开性得到了群的可解性,p-幂零性的判别,同时得到了群系的一些结论.Let G be a finite group. A subgroup H of G is said to be a semi CAP- subgroup of G if there exists a given chief series 1 = G0△G1△……Gn-1△Gn=G such that for every i = 1, 2,..., n, either H covers Gi/Gi-1 or H avoids Gi/Gi-1. In this paper, using the condition that some maximal subgroups or 2-maximal subgroups are semi CAP-subgroups of G, we get some criterions for solvability, and p-nilpotency of G. Meanwhile, we obtain some results about formation.

关 键 词：解群 半CAP-子群 P-幂零性 群系 

分 类 号：O152[理学—数学]