Transitive Partial Hyperbolic Flocks of Deficiency One

Abstract

artial hyperbolic flocks of deficiency one in $PG(3,q)$ are equivalent totranslation planes with spreads in $PG(3,q)$ admitting Baer groups of order $q-1$. In this article, we completely classify the associated derivabletranslation planes of order $p^{4}$, for $p$ a prime, inducing a collineationgroup transitive on the partial flock. There are exactly two possiblenon-linear flocks and planes, those whose planes are the semifield of order$16$ with kernel $GF(4)$ and the plane of order $81$, due to Johnson and Pomareda.