|
|
| |
| On the Wielandt Subgroup in a p-Group of Maximal Class |
| |
Citation： |
Xiaohong ZHANG,Xiuyun GUO.On the Wielandt Subgroup in a p-Group of Maximal Class[J].Chinese Annals of Mathematics B,2012,33(1):83~90 |
| Page view： 2599
Net amount： 2328 |
Authors： |
Xiaohong ZHANG; Xiuyun GUO; |
Foundation： |
the National Natural Science Foundation of China (No. 11071155) and the Key Disciplines of Shanghai Municipality (No. S30104). |
|
|
| Abstract： |
The Wielandt subgroup of a group G, denoted by w(G), is the intersectionof the normalizers of all subnormal subgroups of G. In this paper, the authors showthat 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 K in Gwith K _= 1. Meanwhile, a necessary and sufficient condition for a regular p-group ofmaximal class satisfying w(G) = ζ2(G) is given. Finally, the authors prove that the powerautomorphism group PAut(G) is an elementary abelian p-group if G is a non-abelian pgroupwith elementary ζ(G) ∩ _1(G). |
Keywords： |
p-Groups of maximal class, Wielandt subgroup, Wielandt series, Upper central series |
Classification： |
20D15,20D25,20D30 |
|
|
Download PDF Full-Text
|
|
|
|
