Polycyclic Groups Admitting a Regular Automorphism of Order Four  

作　　者：Tao XU He Guo LIU 

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

出　　处：《Acta Mathematica Sinica,English Series》2017年第4期565-570,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11371124);Youth Foundation of Hebei Educational Committee(Grant Nos.QN2016184 and F2015402033);Graduate Education Teaching Reform Foundation of Hebei University of Engineering(Grant No.161290140004)

摘　　要：Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C;（α;） and G/[G, α;] are both abelian-by-finite.Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g~φ= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C_G(α~2) and G/[G, α~2] are both abelian-by-finite.

关 键 词：Polycyclic group regular automorphism residually finite 

分 类 号：O152[理学—数学]