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We give a generalization of the theory of flocks of hyperbolic quadrics in PG to what is called an -twisted hyperbolic flock in an arbitrary -dimensional projective space over a field . We obtain an equivalence between a set of translation planes with spreads in PG that admit affine homology groups such that the axis and coaxis and one orbit is a twisted regulus. Examples and generalizations are also given.
SL-unitals are unitals of order admitting a regular action of SL on the complement of some block. They can be obtained from affine SL-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine SL-unitals and show that exactly two parallelisms are fixed by all automorphisms. In nonclassical SL-unitals obtained as closures of affine SL-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.