Some properties of central kernel quotient of a group

Abstract

The authors, in 2016, introduced the notion of central autocommutator subgroup of a group [Formula: see text] and proved some new results concerning the central kernel subgroup of [Formula: see text], which was introduced earlier by Haimo in [Formula: see text]. In this paper, we establish some results on central kernel quotient of [Formula: see text]. Finally, we introduce the concept of central autonilpotent (henceforth [Formula: see text]-nilpotent) groups and determine its relationship with the nilpotency of the subgroups of central automorphism of [Formula: see text].