Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online March 10, 2022

Copyright © The Korean Mathematical Society.

Computation of Wedderburn decomposition of groups algebras from their subalgebra

Gaurav Mittal and Rajendra Sharma

IIT Rookee, Indian Institute of Technology, Delhi

Abstract

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: 20C05

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