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.