# On schemes originated from Ferrero pairs

Document Type: Research Paper

Authors

1 Department of‎ ‎Mathematics‎, K‎. ‎N‎. ‎Toosi University of Technology‎, ‎‎

2 K. N. Toosi university of Technology University, Tehran-Iran.

Abstract

‎‎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.

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