Galois extensions ramified only at one prime

This paper gives some restrictions on finite groups that can occur as Galois groups of extensions over Q and over Fq(t) ramified only at one finite prime. Over Q, we strengthen results of Jensen and Yui about dihedral extensions and rule out some non-solvable groups. Over Fq(t) restrictions are given for symmetric groups and dihedral groups to occur as tamely ramified extension over Fq(t) ramified only at one prime.