极大子群数及其型

The Number and Its Type of Maximal Subgroups

有限群的极大子群与原群之间有密切联系。一方面,可以利用极大子群本身的性质来研究原群的结构;另一方面,可以利用极大子群的个数或共轭类数等数量来研究原群的性质。例如,S、Adnan在1979年得出了恰有两个极大子群共轭类的有限群的结构(文[1])。G、Pazderski得到了极大子群数小于21的有限群的可解性(文[2])。G、A、

In this paper we study the properties of a finite group only by the number and its type of the maximal subgroups, we characterise simple groups A_5, A_6, A_7, A_8, A_9 and PSL(2,7) by their types of the number of the maximal subgroups of these groups; and give a simpler proof of the solvability of a finite group with less than 21 maximal subgroups than the proof which was given by Pazderski, G. At the end of this paper we obtain the detailed structure of the finite group with exactly 8 maximal subgroups.