All Questions

What groups can arise as being generated by two rotations in $\mathbb R^2$ by angles $\not \in \mathbb Q\pi$? If the centers of the rotations coincide, then the rotations commute and generate some ...

Definition: Let $h$ be a polynomial in $n$ variables, then : $\gamma(h,r,R):=\{ v \in \mathbb{Z}^{n} : \vert h(v) \vert \leq r, \Vert v \Vert < R \}$ Let $\omega : \mathbb{Z}^{n} \to \{ 0 , 1\}$...

Let $M \in \mathrm{SL}(2, \mathbb{Z}).$ Is there an efficient algorithm to write $M$ as a commutator (group commutator, not algebra commutator) [or fail if this is impossible]? Addendum: answering ...