Regular automorphisms of order p2  

作　　者：Tao XU Heguo LIU 

机构地区：[1]Department of Science,Hebei University of Engineering,Handan 056038,China [2]Department of Mathematics,Hubei University,Wuhan 430062,China

出　　处：《Frontiers of Mathematics in China》2019年第6期1367-1373,共7页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11801129,11771129);the Natural Science Foundation of Hebei Province(No.A2019402211);the Program for Young Top Talent of Higher Learning Institutions of Hebei(No.BJ2018025);the Foundation of Handan(No.1723208068-5);the Excellent Young and Middle-Aged Innovative Team Program of Hubei(No.T201601);the New Century High-Level Talents Foundation of Hubei.

摘　　要：Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG(a^p)and G/[G,a^p]are both nilpotent-by-finite.

关 键 词：Polycyclic group regular automorphism residually finite 

分 类 号：O15[理学—数学]