所有极大子群都为SMSN-群的有限群

摘要

A finite group G is called an SMSN-group if its 2-maximal subgroups are sub-normal in G. In this paper, the author investigates the structure of finite groups which are not SMSN-groups but all their proper subgroups are SMSN-groups. Using the idea of local analysis, a complete classification of this kind of groups is given, which generalizes some results of the structure offinite groups.%若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果.