Every group is the automorphism group of a graph with arbitrarily large genus

Abstract

We prove that, to every abstract group $G$, we can associate a sequence of graphs ${\Gamma }_n$ such that the automorphism group of ${\Gamma }_n$ is isomorphic to $G$ and the genus of ${\Gamma }_n$ is an unbounded function of $n$.

The result is already known, and the available proofs are shorter