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arXiv · 2403.05013

A Note on Fano Planes in Orthogonal Buekenhout-Metz Unitals of Even Order

Wen-Ai Jackson·Peter Wild
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Abstract

An O'Nan configuration in a unital is a set of four lines forming a quadrilateral, where the six intersections of pairs of lines are points of the unital. In 2019 Feng and Li elegantly construct O'Nan configurations in orthogonal and Tits Buekenhout-Metz unitals. We extend their work by extending their construction to a Fano plane embedded in the orthogonal Buekenhout-Metz unital of even order. We deduce that there exist O'Nan configurations in orthogonal Buekenhout-Metz unitals different to those of Feng and Li, and make a conjecture about Fano planes embedded in orthogonal Buekenhout-Metz unitals.

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Wen-Ai Jackson, Peter Wild. 2024-03-08. A Note on Fano Planes in Orthogonal Buekenhout-Metz Unitals of Even Order. https://arxiv.org/abs/2403.05013

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