A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras of Split Metacyclic $p$-groups

Abstract

In this article, we present a concise combinatorial formula for efficiently determining the Wedderburn decomposition of rational group algebra associated with a split metacyclic $p$-group $G$, where $p$ is an odd prime. We also provide a combinatorial formula to count irreducible rational representations of $G$ of distinct degrees.