A short proof of Greenberg's Theorem
Group Theory
2019-12-17 v2
Abstract
Greenberg proved that every countable group is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if is finite. We give a short and explicit algebraic proof of this for finitely generated groups .
Cite
@article{arxiv.1908.06675,
title = {A short proof of Greenberg's Theorem},
author = {Gareth A. Jones},
journal= {arXiv preprint arXiv:1908.06675},
year = {2019}
}
Comments
5 pages. This extends the proof in version 1 for finite groups $A$ to all finitely generated groups $A$. Some citations have been added