On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , ℤ 5 )

Rajendra K. Sharma; Gaurav Mittal

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 1, page 1-10
  • ISSN: 0862-7959

Abstract

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We give the characterization of the unit group of 𝔽 q S L ( 2 , ℤ 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , ℤ 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group ℤ 5 .

How to cite

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Sharma, Rajendra K., and Mittal, Gaurav. "On the unit group of a semisimple group algebra $\mathbb {F}_qSL(2, \mathbb {Z}_5)$." Mathematica Bohemica 147.1 (2022): 1-10. <http://eudml.org/doc/298042>.

@article{Sharma2022,
abstract = {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 $2 \times 2$ matrices having determinant $1$ over the cyclic group $\mathbb \{Z\}_5$.},
author = {Sharma, Rajendra K., Mittal, Gaurav},
journal = {Mathematica Bohemica},
keywords = {unit group; finite field; Wedderburn decomposition},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the unit group of a semisimple group algebra $\mathbb \{F\}_qSL(2, \mathbb \{Z\}_5)$},
url = {http://eudml.org/doc/298042},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Sharma, Rajendra K.
AU - Mittal, Gaurav
TI - On the unit group of a semisimple group algebra $\mathbb {F}_qSL(2, \mathbb {Z}_5)$
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 1
SP - 1
EP - 10
AB - 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 $2 \times 2$ matrices having determinant $1$ over the cyclic group $\mathbb {Z}_5$.
LA - eng
KW - unit group; finite field; Wedderburn decomposition
UR - http://eudml.org/doc/298042
ER -

References

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