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$K_2$ over finite fields and polynomials over finite fields

For the concrete instances that you are considering, the finite field ${\mathbb F}_q$ and the ring of polynomials ${\mathbb F}_q[x]$, the following may help: (i) You have the elementary matrices $e_{...
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$K_2$ over finite fields and polynomials over finite fields

Weibel explains, in Example 5.2.2 of chapter 3 of "The K-book," how to use the Euclidean algorithm and some very concrete linear algebra to show that $K_2(\mathbb{Z})$ is cyclic of order $2$....
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