Abstract
This article investigates cyclic completek-caps in PG(3,q). Namely, the different types of completek-capsK in PG(3,q) stabilized by a cyclic projective groupG of orderk, acting regularly on the points ofK, are determined. We show that in PG(3,q),q even, the elliptic quadric is the only cyclic completek-cap. Forq odd, it is shown that besides the elliptic quadric, there also exist cyclick-caps containingk/2 points of two disjoint elliptic quadrics or two disjoint hyperbolic quadrics and that there exist cyclick-caps stabilized by a transitive cyclic groupG fixing precisely one point and one plane of PG(3,q). Concrete examples of such caps, found using AXIOM and CAYLEY,‡ are presented.
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