Classifying group algebras in which the socle of the center is an ideal

TL;DR

This paper investigates finite group algebras where the socle of the center forms an ideal, providing structural insights and a complete characterization for specific cases.

Contribution

It offers a detailed analysis and a full classification of groups with the property that the socle of their center is an ideal.

Findings

Characterization of groups with socle of center as an ideal

Structural analysis of such group algebras

Complete classification in particular cases

Abstract

This paper extends the study of group algebras of finite groups in which the socle of the center is an ideal. We provide a detailed analysis of the structure of these groups. In a particular case, we reach a complete characterization of the groups with this property.