Abstract
Let G be a finite group. Inspired by the properties of D(G), we define the -norm, denoted by
to be the intersection of the normalizers of the derived subgroups of all subgroups H of G such that H is generated by two elements of G and
is nilpotent. Set
= 1. We define
/
=
for
and we denote by
the terminal term of the ascending series. In this paper, we mainly show that
= D(G).
Keywords:
Acknowledgments
The authors are grateful to Prof. Shirong Li who provided profound suggestions. The authors are grateful to the referee who provided profound suggestions and detailed report.