Factorizations of group determinant in group algebra for any abelian subgroup

TL;DR

This paper extends Dedekind's theorem to broader classes of finite groups, providing new factorizations of group determinants in group algebras, especially for groups with index-two abelian subgroups.

Contribution

It generalizes Dedekind's theorem and offers new insights into irreducible representations and conjugation of group algebras for specific finite groups.

Findings

Extended Dedekind's theorem for broader group classes

Derived corollaries on irreducible representations

Analyzed conjugation of group algebras with index-two abelian subgroups

Abstract

We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finite groups and a conjugation of the group algebra of the groups which have an index-two abelian subgroups.