3 research outputs found
SL(2,q)-Unitals
Unitals of order are incidence structures consisting of points such that each block is incident with points and such that there are unique joining blocks. In the language of designs, a unital of order is a - design. An affine unital is obtained from a unital by removing one block and all the points on it. A unital can be obtained from an affine unital via a parallelism on the short blocks. We study so-called (affine) -unitals, a special construction of (affine) unitals of order where is a prime power. We show several results on automorphism groups and translations of those unitals, including a proof that one block is fixed by the full automorphism group under certain conditions. We introduce a new class of parallelisms, occurring in every affine -unital of odd order. Finally, we present the results of a computer search, including three new affine -unitals and twelve new -unitals