Generalization of Frobenius' theorem for group determinants

TL;DR

This paper generalizes Frobenius' theorem on group determinants, providing new insights into the irreducible representations of finite groups and extending the classical representation theory framework.

Contribution

It introduces a broader version of Frobenius' theorem, enhancing understanding of group determinants and their relation to irreducible representations.

Findings

Generalized Frobenius' theorem for group determinants

Derived new corollary on irreducible representations

Extended classical representation theory results

Abstract

Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobenius' theorem. The generalization leads to a corollary on irreducible representations of finite groups.