摘要
Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is stabilized by OB（A）. As applications, someconditions are given for a finite group to be p-supersolvable.
Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is stabilized by OB（A）. As applications, someconditions are given for a finite group to be p-supersolvable.
基金
The research was partially supported by the National Natural Science Foundation of China （11371237） and a grant of the First-Class Discipline of Universities in Shanghai.
