Finite semisimple group algebra of a normally monomial group

TL;DR

This paper provides a detailed algebraic description and explicit decompositions of finite semisimple group algebras for normally monomial groups, including automorphism groups.

Contribution

It offers the first explicit Wedderburn decomposition for these group algebras and determines their automorphism groups.

Findings

Explicit Wedderburn decompositions for various normally monomial groups

Automorphism groups of the studied group algebras determined

Complete algebraic structure characterized

Abstract

In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group algebras of various normally monomial groups. The automorphism groups of these group algebras are also determined.