On the Intersection of the Normalizers of the Nilpotent Residuals of All Subgroups of a Finite Group

Abstract

In this paper, a characteristic subgroup [Formula: see text] of a finite group G is defined, which is the intersection of the normalizers of the nilpotent residuals of all subgroups of G, and the properties of [Formula: see text] and the relationship between [Formula: see text] and the group G are investigated.