On the equation $x+y=1$ in finitely generated groups in positive characteristic

Peter Koymans, Carlo Pagano

Let $K$ be a field of characteristic $p>0$ and let $G$ be a subgroup of $K^{\ast }\times K^{\ast }$ with ${\text{dim}}_{\mathbb{Q}}(G{\otimes }_{\mathbb{Z}}\mathbb{Q})=r$ finite. Then Volo…