Unitals in $PG(2,q^2)$ with a large 2-point stabiliser

Abstract

Let $\cU$ be a unital embedded in the Desarguesian projective plane $\PG(2,q^2)$. Write $M$ for the subgroup of $\PGL(3,q^2)$ which preserves $\cU$. We show that $\cU$ is classical if and only if $\cU$ has two distinct points $P,Q$ for which the stabiliser $G=M_{P,Q}$ has order $q^2-1$.

Revised version - clarified the case mu\neqλ^{q+1} - 7 pages