次正规子群对群结构的影响  

The Influence of Subnormal Subgroups on The Structure of Groups

作　　者：金程程 海进科[1] 张培鑫[1] 

机构地区：[1]青岛大学数学与统计学院

出　　处：《青岛大学学报（自然科学版）》2016年第3期8-10,15,共4页Journal of Qingdao University(Natural Science Edition)

摘　　要：研究了次正规子群对有限群结构的影响,得到了有限可解群的若干充分条件。讨论了由两个子群所生成群的可解性及有限性问题,证明了如果G是由两个有限可解子群H,K所生成的群,且H次正规于G,则G为有限可解群。The purpose is to investigate the influence of subnormal subgroup on finite groups. Some sufficientconditions of soluble finite groups was obtained. The finiteness and solubility of the groups whichgenerated by two subgroups is discussed. Suppose that G is generated by two finite soluble subgroups Hand K , and H is subnormal in G. Then G is finite soluble group.

关 键 词：次正规子群 可解群 群列 

分 类 号：O152.6[理学—数学]