Embeddings of Ree unitals in a projective plane over a field

2020/07/20 by Nagy, Gábor P. · 1 citation
#05B05 #51E20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.10464

Abstract

We show that the Ree unital R(q) has an embedding in a projective plane over a field F if and only if q=3 and \mathbbF₈ is a subfield of F. In this case, the embedding is unique up to projective linear transformations. Besides elementary calculations, our proof uses the classification of the maximal subgroups of the simple Ree groups.

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

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