On unit group of finite semisimple group algebras of non-metabelian groups of order 108

Year 2021, Volume: 8 Issue: 2, 59 - 71, 20.05.2021

Gaurav Mittal Rajendra. K. Sharma

https://doi.org/10.13069/jacodesmath.935938

Cited By: 1

Abstract

In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian. We consider all the non-metabelian groups of order $108$ and find the Wedderburn decomposition of their semisimple group algebras. And as a by-product obtain the unit groups.

Keywords

Unit group, Finite field, Wedderburn decomposition

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