Unitals without O'Nan configurations are classical if they admit all translations

TL;DR

This paper proves that finite unitals admitting all translations and lacking O'Nan configurations must be classical, specifically isomorphic to the Hermitian unital, thus characterizing their structure.

Contribution

It establishes a characterization of classical unitals based on translation properties and the absence of O'Nan configurations, extending understanding of their geometric structure.

Findings

Unitals with all translations and no O'Nan configurations are classical.

Such unitals are isomorphic to Hermitian unitals.

Provides a new criterion for identifying classical unitals.

Abstract

We prove the statement in the title: if a (finite) unital admits all translations and contains no O'Nan configurations then the unital is classical, i.e., isomorphic to the Hermitian unital of the same order.