FerreroPair

A Ferrero pair is an ordered pair $(N,\Phi)$ where $N$ is an additive written but not necessarily abelian group and $\Phi$ is a collection of fixed point free automorphisms of $N$. There are several constructions of designs via Short difference families? that give us designs from Ferrero pairs. There are many properties of the resulting designs that are implied by the structure of the pair. The Spectrum of finite Ferrero pair is understood.