A short note on Wedderburn decomposition of a group algebra

Abstract

In this paper, we extend the result of Mittal and Sharma (Bull. Korean Math. Soc. 2022) on Wedderburn decomposition (WD) of a finite semisimple group algebra. It is known that, under certain conditions, WD of a finite semisimple group algebra $F_{q}G$ can be computed from WD of its subalgebra $F_q(G/H)$, where $H$ is a normal subgroup of $G$ of prime order and $q=p^k$ for some prime $p$ and positive integer $k$. We extend this result to any normal subgroup $H$ of $G$ of order $n$.