On Normalized Table Algebras Generated by a Faithful Non-real Element of Degree 3-II

TL;DR

This paper classifies finite groups with a faithful non-real irreducible character of degree 3 by studying normalized table algebras generated by such elements, avoiding traditional character theory methods.

Contribution

It introduces a new approach using normalized table algebras to classify specific finite groups, bypassing classical character theory.

Findings

Classification of finite groups with a faithful non-real irreducible character of degree 3

Development of a framework for studying table algebras generated by degree 3 elements

Open cases remaining in the theory of normalized table algebras

Abstract

The concept of "table algebra" was introduced by Z Arad anf H. Blau in order to study in a uniform way properties of products of conjugacy classes and of irreducible characters of a finite group, Except for certain cases which remain open, Normalized Table Algebras Generated by a Faithful Non- real Element of degree 3. As application we classified finite groups with a faithful non-real irreducible character of dimension 3 without using character theory of finite groups.