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

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

2010-09-30

arxiv.org/abs/1009.6109v3

Mathematics

Combinatorics

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

Scientific paper

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 $q^2-1$.

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