A classification of unitals in nearfield planes with maximal automorphism group

TL;DR

This paper classifies certain geometric structures called parabolic unitals in nearfield planes with maximal symmetry, and explores broader results under less restrictive conditions.

Contribution

It provides a complete classification of parabolic unitals with maximal automorphism group in regular nearfield planes of odd order.

Findings

Classified parabolic unitals with maximal automorphism group in nearfield planes.

Established general results for parabolic unitals under weaker assumptions.

Identified structural properties of unitals related to their automorphism groups.

Abstract

We classify the parabolic unitals in regular nearfield planes of odd order $q^2$ whose linear collineation group has the maximal size of $q^3-q$. We also establish a number of more general results concerning parabolic unitals in regular nearfield planes under weaker assumptions.