Automorphisms of abelian group extensions

TL;DR

This paper investigates the conditions under which automorphisms of subgroups and quotient groups in abelian extensions can be extended or lifted to automorphisms of the entire group, enhancing understanding of their structural symmetries.

Contribution

It provides new criteria and methods for extending automorphisms from components to the whole abelian extension, addressing a fundamental problem in group theory.

Findings

Established conditions for extending automorphisms of N to G

Derived criteria for lifting automorphisms of H to G

Enhanced understanding of automorphism structures in abelian extensions

Abstract

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.