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

S. Maheshwari; R. K. Sharma

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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A note on units in FqSL(2,Z3)\mathbb{F}_q SL(2, \mathbb{Z}_3)

Abstract

References

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