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