Construction of the smallest Ree-Tits unital from the special linear group of degree two over the field with eight elements

TL;DR

This paper constructs the smallest Ree-Tits unital using matrix groups related to Ree groups over a finite field, providing explicit configurations and embeddings into larger structures.

Contribution

It introduces a matrix-based construction of the smallest Ree-Tits unital and details explicit embeddings into larger unitals, advancing understanding of these combinatorial structures.

Findings

Explicit matrix description of the smallest Ree-Tits unital

Configurations within the unital determined through computations

Embeddings into larger Ree-Tits unitals explicitly constructed

Abstract

We construct the smallest Ree-Tits unital from a group of matrices that is isomorphic to the commutator group of the corresponding Ree group. The matrix description is used to determine configurations in the unital via explicit computations. Embeddings into larger Ree-Tits unitals are made explicit.