The arithmetic-groups tag has no usage guidance.

**13**

votes

**2**answers

421 views

### Minimal number of generators for $GL(n,\mathbb{Z})$

$\DeclareMathOperator{\gl}{GL}\DeclareMathOperator{\sl}{SL}$From de la Harpe's book "Topics in Geometric Group Theory" I learnt that $\gl(n,\mathbb{Z})$ is generated by the matrices $$s_1 = ...

**10**

votes

**2**answers

1k views

### Why are $S$-arithmetic groups interesting?

Let $K$ be a number field and $S$ a finite set of valuations of $K$, including $\infty$.
Define the $S$-numbers $K_S$ to be the direct product $\prod_{s \in S} K_s$ where $K_s$ denotes the completion ...