On the Norm and Wielandt Series in Finite Groups

Abstract

The norm N(G) of a group G is the intersection of the normalizes of all the subgroups of G. A group is called capable if it is a central factor group. In this paper, we give a necessary and sufficient condition for a capable group to satisfy N(G)=ζ(G), and then some sufficient conditions for a capable group with N(G)=ζ(G) are obtained. Furthermore, we discuss the norm of a nilpotent group with cyclic derived subgroup.