A note on units in $\mathbb{F}_q SL(2, \mathbb{Z}_3)$

  • S. Maheshwari KIET Group of Institutions Delhi-NCR, Ghaziabad, India
  • R. K. Sharma Indian Inst. Technology Delhi, India
Keywords: Group Algebra, Unit Group, Finite Field

Abstract

UDC 512.5

Let $R$ be a ring, and $ SL(2,R)$ be the special linear group of $2\times2$ matrices with determinant $1$ over $R$.
We obtain the Wedderburn decomposition of
$\dfrac{\mathbb{F}_q SL(2,\mathbb{Z}_3)}{J(\mathbb{F}_q SL(2,\mathbb{Z}_3))}$ and show that $ 1+J(\mathbb{F}_q SL(2,\mathbb{Z}_3))$ is a non-Abelian group, where $\mathbb{F}_q$ is a finite field with $q = p^k$ elements of characteristic $2$ and $3.$

 

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Published
18.08.2021
How to Cite
Maheshwari , S., and R. K. Sharma. “A Note on Units in $\mathbb{F}_q SL(2, \mathbb{Z}_3)$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 8, Aug. 2021, pp. 1147 -52, http://umj.imath.kiev.ua/index.php/umj/article/view/588.
Section
Short communications