On unit group of finite semisimple group algebras of non-metabelian groups of order 108
DOI:
https://doi.org/10.13069/jacodesmath.935938Keywords:
Unit group, Finite field, Wedderburn decompositionAbstract
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.
Received: 30 July 2020 | Accepted: 20 October 2020Downloads
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