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.