有限群的极大子群的正规指数

有限群的结构与其子群性质间的关系问题是群论的一个重要研究方向,通过群的极大子群、正规子群、半正规子群、极大子群的正规指数等去研究群的可解性,超可解性、幂零性等,已有一系列结果.应用极小反例方法,利用有限群极大子群的正规指数,得到了一个有限群是π-可解群的充分条件,2个有限群是π-可解群的充分必要条件.

On the Normal Index of Maximal Subgroups in Finite Groups

The connection between the structure of finite group and character of subgroup in finite group is important in research.A series of results of solubility,super solubility,nilpotent of groups is obtained by researching the maximal subgroup,normal subgroup,subnormal subgroup,and normal index of maximal subgroup in finite group.With the method of the normal index of maximal subgroup of a finite group and minimal inverse example,one sufficient condition of finite group as π-soluble group,and two necessary and sufficient conditions of finite group as π-soluble group are obtained.