Sharply transitive subsets of P?L(2,F) and spreads covered by derivable partial spreads

Abstract

It is well known that one can associate a spread and hence a translation plane with every flock of a Miquelian Minkowski plane. If the Miquelian Minkowski plane is described via the sharply 3-fold transitive action of the projective group PGL(2,F) on the projective line over the commutative fieldF then the flocks correspond to sharply transitive subsets of PGL(2,F). We show that under certain conditions one can also associate a spread with a sharply transitive subset of PΓL(2,F) where PΓL(2,F) acts on the projective line over the not necessarily commutative fieldF in the natural way.