Partial spreads over Zq

AbstractLet p be a prime, q = pa, and G = Z2nq. We consider partial spreads in G, i.e. collections of pairwise disjoint subgroups of order qn. It is shown that the maximum size of such a collection is exactly pn + 1. The method of proof consists in representing partial spreads in G by invertible n×n matrices over Zq and in finding a close relation to (ordinary) partial spreads over Zp. Geometrically, partial spreads over Zq correspond to homogeneous translation nets