A note on the conjecture of the autotopism group of the Figueroa’s presemifields

• Autores: Meléndez Florián, Walter J., Delgado Olórtegui, Moisés R.
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: inglés
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/3115
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3115
• Nivel de acceso: acceso abierto
• Materia: Presemicuerpo finito; semicuerpo finito; grupo autotopismo; semicuerpo de Cordero-Figueroa; presemicuerpo de Figueroa; Finite presemifield; finite semifield; autotopism group; Cordero-Figueroa semifield; Figueroa’s presemifield

In [4] was stated the following conjecture: If a Figueroa’s presemifield P(K; alfa; beta; A;B) admits an autotopism of order a p-primitive prime divisor of p^n-1, then its autotopism group is isomorphic to a subgroup of GL(K) x GL(K). In [5] this conjecture was settled under an additional normality condition. In this article, we show that the assumption in the hypothesis of the conjecture is necessary in the sense that there exist a Figueroa’s presemifield, that does not admit such autotopism, for which the conjecture is not met.