On a conjecture about the autotopism group of the Figueroa's presemifields of order

doi:10.1285/i15900932v38n2p11

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

Walter Meléndez, Moisés Delgado

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.

DOI Code: 10.1285/i15900932v38n2p11

Keywords: finite presemifield; finite semifield; autotopism; autotopism group; Cordero-Figueroa semifield; Figueroa's presemifields

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