Unitals with many involutory translations

TL;DR

This paper characterizes classical hermitian unitals by the property that every point is fixed by some non-trivial translation, especially when an involutory translation exists.

Contribution

It provides a new characterization of classical hermitian unitals based on translation properties and involutions.

Findings

Every point fixed by a non-trivial translation implies the unital is classical.

Existence of an involutory translation further characterizes the unital as hermitian.

The result links translation symmetries to the classical structure of unitals.

Abstract

If every point of a unital is fixed by a non-trivial translation and at least one translation has order two then the unital is classical (i.e., hermitian).