Bull. Korean Math. Soc. 2022; 59(3): 781-787
Online first article March 10, 2022 Printed May 31, 2022
https://doi.org/10.4134/BKMS.b210478
Copyright © The Korean Mathematical Society.
Gaurav Mittal, Rajendra Kumar Sharma
IIT Roorkee; IIT Delhi
In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra $\mathbb{F}_qG$ can be deduced from a subalgebra $\mathbb{F}_q(G/H)$ of factor group $G/H$ of $G$, where $H$ is a normal subgroup of $G$ of prime order $P$. Here, we assume that $q=p^r$ for some prime $p$ and the center of each Wedderburn component of $\mathbb{F}_qG$ is the coefficient field $\mathbb{F}_q$.
Keywords: Wedderburn decomposition, unit group, finite field
MSC numbers: Primary 20C05
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