子群的完全c-可换性与p-可分群  

Completely c-Permutable Subgroups and p-Decomposable Group

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：《四川理工学院学报（自然科学版）》2009年第4期20-22,共3页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10771180)

摘　　要：设■表示P-可分群的群类。利用完全c-可换子群的概念,得到了P-可分群的两个充分条件:(1)如果群G的4阶循环子群在G中完全c-可换且G的任意极小子群含于Z_■(G)中,那么G是P-可分群;(2)设H■G且G/H是P-可分群。如果H的任意阶循环子群在中完全c-可换且H的任意极小子群包含在Z■(G)中,那么G是p-可分群。Let φ be the class of all p-decomposable groups. Using the concept, completely c-permutable subgroup of finite groups, two sufficient conditions of p-decomposable group 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 φ-hypercenter of G, then G is a p-decomposable group ; （2） Let H be a normal subgroup of G and G/H be a p-decomposable group. If any cyclic subgroup of H of order 4 is completely c-permutable in G and any minimal subgroup of H is contained in φ-hypercenter of G, then G is a p-decomposable group.

关 键 词：有限群 完全c-可换子群 极小子群 p-可分群 

分 类 号：O152.1[理学—数学]