On the unit group of a semisimple group algebra $\ bb{Z}_5

We give the characterization of the unit group of $\mathbb{F}_qSL(2, \mathbb{Z}_5)$, where $\mathbb{F}_q$ is a finite field with $q = p^k$ elements for prime $p > 5,$ and $SL(2, \mathbb{Z}_5)$ denotes the special linear group of $2 \times2$ matrices having determinant $1$ over the cyclic group $\...

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Bibliographic Details
Published inMathematica bohemica Vol. 147; no. 1; pp. 1 - 10
Main Authors Rajendra K. Sharma, Gaurav Mittal
Format Journal Article
LanguageEnglish
Published Institute of Mathematics of the Czech Academy of Science 01.04.2022
Subjects
finite field
unit group
wedderburn decomposition
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Summary:We give the characterization of the unit group of $\mathbb{F}_qSL(2, \mathbb{Z}_5)$, where $\mathbb{F}_q$ is a finite field with $q = p^k$ elements for prime $p > 5,$ and $SL(2, \mathbb{Z}_5)$ denotes the special linear group of $2 \times2$ matrices having determinant $1$ over the cyclic group $\mathbb{Z}_5$.
ISSN:0862-7959
2464-7136
DOI:10.21136/MB.2021.0104-20