On the Wielandt Subgroup in a p-Group of Maximal Class  

作　　者：Xiaohong ZHANG Xiuyun GUO 

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

出　　处：《Chinese Annals of Mathematics,Series B》2012年第1期83-90,共8页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 11071155);the Key Disciplines of Shanghai Municipality (No. S30104)

摘　　要：The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζi（G） for all integer i or wi（G） = ζi＋1（G） for every integer i, and w（G/K） = ζ（G/K） for every normal subgroup g in G with K ≠ 1. Meanwhile, a necessary and sufficient condition for a regular p-group of maximal class satisfying w（G） = ζ2（G） is given. Finally, the authors prove that the power automorphism group PAut（G） is an elementary abelian p-group if G is a non-abelian p- group with elementary ζ（G） ∩ζ1（G）.

关 键 词：p-Groups of maximal class Wielandt subgroup Wielandt series Uppercentral series 

分 类 号：O178[理学—数学] O152.1[理学—基础数学]