极小子群的完全条件置换性与有限群的超可解  

Completely Conditional Permutability of Minimal Subgroupsand Supersolubility of Finite Groups

作　　者：查明明[1] 

机构地区：[1]淮海工学院数理系,江苏连云港222005

出　　处：《徐州师范大学学报（自然科学版）》2004年第3期1-3,共3页Journal of Xuzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10171086)

摘　　要：〈H,T〉表示由H和T生成的G的子群,即群G的包含H和T的最小子群.群G的子群H称为G中的完全条件置换子群,如果对G的任意子群T,存在元素x∈〈H,T〉,使HTx=TxH.利用极小子群的完全条件置换性给出了一个群为超可解群的判别准则:设G是有限群,N G,且G/N超可解,若N的所有极小子群及4阶循环子群都是G的完全条件置换子群,则G是一个超可解群.〈H,T〉 denotes the subgroup of G generated by H and T,which is the smallest subgroup of G containing H and T.The subgroup H of a group G is called completely conditionally permutable in G if for every subgroup T of G there exists an element x∈〈H,T〉 such that HT^x=T^xH.In this paper,a sufficient condition for supersolubility of groups is given by using the completely conditionally permutability of minimal subgroups:Let G is a finite group,NG,and G/N is supersoluble.If every minimal subgroup and every cyclic subgroup of order 4 of N are completely c-permutable in G,then G is supersoluble.

关 键 词：极小子群 完全条件置换子群 有限群 超可解群 

分 类 号：O152.1[理学—数学]