On the inverse Galois problem - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T14:06:04Z http://mathoverflow.net/feeds/question/70155 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/70155/on-the-inverse-galois-problem On the inverse Galois problem Hugo Chapdelaine 2011-07-12T17:39:17Z 2011-07-12T19:52:50Z <p>Q: What is the "simplest" finite group $G$ for which we don't know how to realise it as a Galois group over $\mathbf{Q}$ ?</p> <p>So here the word simplest might be interpreted in a broad sense. If you want something precise you may take the group of smallest order but I prefer to leave the question as it is. Also since naturally one classifies finite groups into families one may also ask the following</p> <p>Q: What is the "simplest" example of a family of finite groups for which the inverse Galois problem is unknown?</p> http://mathoverflow.net/questions/70155/on-the-inverse-galois-problem/70169#70169 Answer by Felipe Voloch for On the inverse Galois problem Felipe Voloch 2011-07-12T19:52:50Z 2011-07-12T19:52:50Z <p>I am not an expert and I might be misrembering some talks I've attended. Anyway, $SL_2(\mathbb{F}_q)$ can be done for prime $q$ by using torsion on non-CM elliptic curves. But I don't think it's been done for general prime powers $q$. Also, what about $SL_3$? </p>