Abelian Groups, Homomorphisms and Central Automorphisms of Nilpotent Groups

TL;DR

This paper establishes a precise condition under which finite nilpotent groups possess an abelian group of central automorphisms, advancing understanding of automorphism structures in group theory.

Contribution

It provides a necessary and sufficient criterion for finite nilpotent groups to have abelian central automorphism groups, a novel characterization in the field.

Findings

Derived a necessary and sufficient condition for abelian central automorphism groups

Enhanced understanding of automorphism structures in finite nilpotent groups

Contributed to classification criteria in group theory

Abstract

In this paper we find a necessary and sufficient condition for a finite nilpotent group to have an abelian central automorphism group.