Fixed-point-free automorphism groups from rings

Fixed-point-free automorphism groups of groups arise in Frobenius groups, planar nearrings, difference family constructions of 2--designs and the study of CP groups. Several examples of fpf automorphism groups have been derived from rings. In this note, we demonstrate that numerically, all finite examples can be so derived and that all fpf automorphism groups of abelian groups can be embedded into ring-generated examples.