The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$

R. K. Sharma; Yogesh Kumar; D. C. Mishra

doi:10.3842/umzh.v76i7.7500

Authors

R. K. Sharma Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India
Yogesh Kumar Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India
D. C. Mishra Department of Mathematics, Govt. P. G. College Jaiharikhal, Uttrakhand, India

DOI:

https://doi.org/10.3842/umzh.v76i7.7500

Keywords:

Group algebra, Wedderburn Decomposition, Unit Group.

Abstract

UDC 512.5

Let $p$ be a prime, $\mathbb{F}_q$ be a finite field with $q=p^n$ elements, and $\mathbb{Z}_9\rtimes\mathbb{Z}_3$ be the semidirect product of the groups $\mathbb{Z}_9$ and $\mathbb{Z}_3$ . The unit group $\mathcal{U}(\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ of the group algebra $\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ is completely characterized.

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The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$

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The unit group of the group algebra Fq(Z9⋊Z3)\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)

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The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$