Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ from a subalgebra of factor group of $G$

Authors : Gaurav MITTAL, Rajendra Kumar SHARMA

Pages : 91-100

Doi:10.24330/ieja.1077582

View : 14 | Download : 10

Publication Date : 2022-07-16

Article Type : Research Paper

Abstract :In this paper, we derive a condition under which the Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ can be deduced from the Wedderburn decomposition of $\mathbb{F}_qinsert ignore into journalissuearticles values(G/H);$, where $H$ is a normal subgroup of $G$ having two elements and $q=p^k$ for some prime $p$ and $k\in \mathbb{Z}^+$. In order to complement the abstract theory of the paper, we deduce the Wedderburn decomposition and hence the unit group of semisimple group algebra $\mathbb{F}_qinsert ignore into journalissuearticles values(A_5\rtimes C_4);$, where $A_5\rtimes C_4$ is a non-metabelian group and $C_4$ is a cyclic group of order $4$.
Keywords : Wedderburn decomposition, unit group, finite field