ON SCHEMES ORIGINATED FROM FERRERO PAIRS

The Frobenius complement of a given Frobenius group acts on its kernel. The scheme which is arisen from the orbitals of this action is called Ferrero pair scheme. In this paper, we show that the fibers of a Ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality. Moreover, it is shown that the restriction of a Ferrero pair scheme on each fiber is isomorphic to a regular scheme. Finally, we prove that for any prime p, there exists a Ferrero pair p-scheme, and if p > 2, then the Ferrero pair p-schemes of the same rank are all isomorphic.