The Multiplicative Automorphisms of a Finite Nearfield, with an Application

Abstract

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that these results can be used in order to count the number of near vector spaces of a given dimension over a given nearfield, up to isomorphism.