ABSTRACT
In the previous chapter, we considered 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 par tial spread is not necessarily derivable. Although our manner of construction is completely independent from that of Sandler [75], the constructed ‘semi field 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 5L(2,g). These 5L(2,g)-spreads and their parent or related semifields have also been described in a completely different manner in the work of Glynn [26].
