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Three new examples of non-linear flocks of the non-singular ruled quadric Q+(3,q) of PG(3,q) are given.
Abstract The prove that a non-hyperelliptic flock of the quadratic cone, the associated translation plane of which is either a semifield or a likeable plane, is isomorphic to one of the known… (More)
We construct the new semifield flock ofPG(3, 243) associated with the Penttila?Williams translation ovoid ofQ(4, 243) and we study the associated generalized quadrangle and its translation dual.
We discuss infinite elation generalized quadrangles as group coset geometries and use this approach to deal with the special case of those associated with flocks of quadratic cones of PG(3,K).
A complete characterization of the flocks of Q+(3, q) is given. As an application, it follows that if q is odd, q≠11, 23, 59, there exist no maximal exterior sets of Q+ (2n−1, q) for n>2.
We give a characterization of translation ovoids of flock generalized quadrangles. Then we prove that, if q = 2e, each elation generalized quadrangle defined by a flock has a large class of… (More)