A short proof of Greenberg's Theorem

Abstract

Greenberg proved that every countable group $A$ is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if $A$ is finite. We give a short and explicit algebraic proof of this for finitely generated groups $A$.

arXiv comment5 pages. This extends the proof in version 1 for finite groups $A$ to all finitely generated groups $A$. Some citations have been added