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On a conjecture about the autotopism group of the Figueroa’s presemifields of order \(p^n\). (English) Zbl 1428.12010

Summary: In [Discuss. Math., Gen. Algebra Appl. 36, 117–126 (2016)] the authors and R. Figueroa 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 \(K = \mathrm{GF}(3^6)\). 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.

MSC:

12K10 Semifields
17A35 Nonassociative division algebras
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References:

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