All Questions

Suppose $G$ is a finite subgroup of $\mathrm{GL}(n,\mathbb{Q})$. For a set $\mathcal{M} \subseteq G$ that generates $G$, define the $\mathcal{M}$-diameter $\mathit{diam}(G, \mathcal{M})$ of $G$ to be ...

Let $R\subset\mathbb{C}$ be a subring, and let $A,B\in SL(2,\mathbb{C})$ be matrices such that $A,B,AB$ all have trace in $R$. For which $R$ can we then deduce that $A,B$ are simultaneously conjugate ...