Cyclic 2-Spreads in $V(6,q)$ and Flag-Transitive Affine Linear Spaces

TL;DR

This paper classifies certain cyclic spreads in a 6-dimensional vector space over finite fields, addressing a key open case in the classification of flag-transitive linear spaces using polynomial methods.

Contribution

It provides a complete classification of cyclic 2-spreads in V(6,q) with transitive cyclic group actions, solving an open problem in flag-transitive linear space classification.

Findings

Complete classification of cyclic 2-spreads in V(6,q)

Addresses open case in flag-transitive linear spaces

Utilizes polynomial approach for classification

Abstract

In this paper we completely classify spreads of 2-dimensional subspaces of a 6-dimensional vector space over a finite field of characteristic not two or three upon which a cyclic group acts transitively. This addresses one of the remaining open cases in the classification of flag-transitive linear spaces. We utilise the polynomial approach innovated by Pauley and Bamberg to obtain our results.