ABSTRACT
In this section, we construct a semifield plane S⊥ with spread in PG(3, q) from a spread S with spread in PG(3, q). S⊥ is called the ‘translation dual’. This concept is explicated in Lunardon [947], and this concept grows out the similar idea of a translation dual of a generalized quadrangle due to J.A. Thas, wherein symplectic semifield spreads and semifield flock spreads are connected. In Chapter 82 on symplectic spreads, we discussed the general construction of semifield 5th cousins and pointed out that semifield flock spreads are equivalent to symplectic semifield spreads in PG(3, q). It is also true that the translation dual of a semifield flock spread is symplectic (see Lunardon [947]). However, there have been no concrete connections between the translation dual of a semifield spread in PG(3, q) and its 5th cousin.
