2 problems

Rosenberger's conjecture. If $G$ is a generalised triangle group, then either $G$ is virtually solvable or $G$ contains a non-abelian free subgroup.

Let $m$ be an odd integer with $m\geq 5$, and let $W\in\mathbb{Z}_2*\mathbb{Z}_4$. Let $\tau_W(\lambda)$ denote the trace polynomial associated with $W$. The trace-polynomial nonex…