The Action on p-Groups and p-Supersolvability  

作　　者：Pengfei Bai Xiuyun Guo Boru Zhang 

机构地区：[1]Department of Mathematics, Shanghai University, Shanghai 200444, China

出　　处：《Algebra Colloquium》2017年第4期685-696,共12页代数集刊（英文版）

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.

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.

关 键 词：action maximal class p-group p-supersolvability 3p-permutability 

分 类 号：O1[理学—数学]