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Questions about the branch of algebra that deals with groups.

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How does $SL_2(\mathbb Z[\sqrt 2])$ embed into $SL(2,\mathbb R)\times SL(2,\mathbb R)$, and ...

I am trying to learn arithmetic groups, from a dynamical point of view. These questions (maybe silly) come to my mind, but I do not know the answer. How does $SL_2(\mathbb Z[\sqrt 2])$ embed into $S …
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