The Multiplicative Automorphisms of a Finite Nearfield, with an Application

Abstract

In this article, we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups and use 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.

Key Words:

• Automorphism
• Counting
• Nearfield
• Near vector space

2010 Mathematics Subject Classification:

• 16Y30
• 12K05
• 20B25

ACKNOWLEDGMENTS

We would like to thank Peter Mayr and the referee for some very useful suggestions.