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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 order16 with kernel GF(4) and the plane of order 81, due to Johnson and Pomareda.


DOI Code: 10.1285/i15900932v29n1p89

Keywords:
51E23; 51A40

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