The Action on p-Groups and p-Supersolvability

• 来源期刊: 代数集刊（英文版）
• 关键词: action maximal class p-group p-supersolvability (3)p-permutability
• 年，卷（期）: 2017,（4）
• 页码范围: 685-696
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386717000451

摘要

Let a finite group A act on a finite p-group P with |P| ＞ pe,where e is an integer with e ≥ 2.In this paper,we show that P is centralized by Op(A(x)p-1) if every non-maximal class p-group of order pe in P is stabilized by Op(A).As applications,some conditions are given for a finite group to be p-supersolvable.