Partial spreads over [formula omitted

Abstract

Let p be a prime, q = p a , and G = Z 2n q . We consider partial spreads in G, i.e. collections of pairwise disjoint subgroups of order q n . It is shown that the maximum size of such a collection is exactly p n + 1. The method of proof consists in representing partial spreads in G by invertible n× n matrices over Z q and in finding a close relation to (ordinary) partial spreads over Z p . Geometrically, partial spreads over Z q correspond to homogeneous translation nets.