There are a couple of beautiful results in finite group theory that look trivial, at least on a first glance, but require non-trivial facts to prove. I am basically interested in whether these results ...
In a recent question of mine I asked whether every infinite group is (isomorphic to) the automorphism group of a graph. The finite case was done by Frucht in 1939. The first answer to this ...
Frucht showed that every finite group is the automorphism group of a finite graph. The paper is here. The argument basically is that a group is the automorphism group of its (colored) Cayley graph ...