On a conjecture about the autotopism group of the Figueroa's presemifields of order $p^n$

Abstract

In [14] was proved that the autotopism group of the Cordero-Figueroa semifield of order $3^6$ is isomorphic to a subgroup of $\Gamma L(K) \times \Gamma L(K)$, where $K = GF(3^6)$. Also a conjecture was proposed for the general case, the autotopism group of a Figueroa's presemifield of order $p^n$. In this article, under a normality condition, we prove this conjecture.