Group Extensions and Automorphism Group Rings

TL;DR

This paper investigates the structure of the automorphism group rings of p-groups by analyzing automorphism groups of their subgroups and quotient groups, providing new insights into their algebraic properties.

Contribution

It introduces a novel approach to understanding automorphism group rings of p-groups through subgroup and quotient analysis, advancing the theoretical framework.

Findings

Characterization of automorphism group rings for specific p-groups

Identification of structural patterns in automorphism groups

New algebraic invariants related to subgroup automorphisms

Abstract

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.