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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.

DOI Code: 10.1285/i15900932v38n2p11

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

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