关于有限群超可解性的一种新判定方法

On Some New Criterion of Supersolvability of Finite Groups

利用子群的弱s-置换性质研究超可解子群的积的问题,并给出群的超可解性的一些判别方法。设群G可以表示为2个子群A和B的积,A在G中拟正规且B为超可解,如果A的Sylow子群的所有极大子群在G中弱s-置换,则G为超可解群。从而得到1个群为超可解群的这样的一种新判别法。

We use weak s-permutation subgroups to study the problem about solvable subgroup,and give some new criterion of supersolvability of finite groups. Suppose that a group G is a product of two subgroups,A and B,where A is quasinormal in G and B is supersolvable. If every maximal subgroup of every Sylow subgroup of A is weak s-permutable in G,then G is supersolvable. Then a new criterion of supersolvability of finite groups is obtained.