ABSTRACT
In Chapter 33, we consider extensions of derivable partial spreads which are necessarily Desarguesian. In this chapter, we consider a similar study of extensions of rational Desarguesian partial spreads but here the partial spread is not necessarily derivable. Although our manner of construction is completely independent from that of Sandler [1147], the constructed ‘semifield spreads’ bear a resemblance to those given by Sandler so we suspect there is more than a coincidental intersection. We shall be constructing semifields of order qn whose spreads contain a Desarguesian partial spread of degree q + 1. However, when n = 3, we here also describe some definitely non-semifield translation planes of order q3 that admit a collineation group isomorphic to SL(2, q). These SL(2, q)-spreads and their parent or related semifields have also been described in a completely different manner in the work of Glynn [402].
