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.
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.
