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

2025/06/03 by Stroppel, Markus Johannes
#20D06 #51E26 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2506.02732

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.

Citations

• Embeddings of Ree unitals in a projective plane over a field
• The norm of a Ree group

Related

• An explicit embedding of the Tits group in the compact real form of E₆
• Embeddings of Ree unitals in a projective plane over a field
• An analogue of a result of Tits for linear and symplectic transvection groups
• On quantitative structure of small Ree groups
• The automorphism group of the group of unitriangular matrices over a field