有限群的完全c-置换子群与超可解性  

Completely c-permutable Subgroups and Supersolubility of Finite Groups

作　　者：刘玉凤[1] 

机构地区：[1]山东工商学院数学与信息科学学院,山东烟台264005

出　　处：《河北北方学院学报（自然科学版）》2012年第5期1-3,共3页Journal of Hebei North University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11071147)

摘　　要：利用完全c-置换子群的概念,得到了有限群超可解的两个充分条件:(1)如果群G的4阶循环子群在G中完全c-置换且G的任意极小子群含于G的超可解超中心Zμ(G)中,那么G是超可解群;(2)设NG且G/N是超可解群。如果N的任意4阶循环子群在G中完全c-置换且N的任意极小子群包含在G的超可解超中心Zμ(G)中,那么G是超可解群。Using the concept of completely c-permutable subgroup,two sufficient conditions of supersoluble finite groups are obtained:(1)If any cyclic subgroup of G of order 4 is completely c-permutable in G and any minimal subgroup of G is contained in the supersoluble hypercenter of G,then G is a supersoluble group;(2)Let N be a normal subgroup of G and G/N be a supersoluble group.If any cyclic subgroup of N of order 4 is completely c-permutable in G and any minimal subgroup of N is contained in supersoluble hypercenter of G,then G is a supersoluble group.

关 键 词：有限群 完全c-置换子群 极小子群 循环子群 超可解超中心 超可解群 

分 类 号：O152.1[理学—数学]