On the autotopism group of the commutative Dickson semifield $K$ and the stabilizer of the Ganley unital embedded in the semifield plane $\Pi(K)$

Abstract

Two methods, one algebraic and one geometric, are given to determine the autotopism group of the commutative Dickson semifield, completing a result of Sandler. The collineation stabilizer subgroup of the embedded Ganley unital is exhibited as a semidirect product whose factor groups are semidirect products of abelian groups.