Перевод названия: LINEAR AUTOTOPISMS OF THE SEMIFIELD PROJECTIVE PLANE
Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: Перспективы развития фундаментальных наук; Томск; Томск
Год издания: 2023
Аннотация: A semifield is a simple ring where the nonzero elements, by multiplication, form a loop. A projective plane is called semifield if its coordinatizing set is a semifield. We consider the problem of classifying finite semifields and the well-known conjecture of Daniel Hughes (1959) on the solvability of the collineation group for a fПоказать полностьюinite non-Desarguesian semifield plane. The information on autotopisms, that is, collineations fixing a triangle, is of great importance. We study autotopisms of even order in the case when the coordinatizing semifield is a two-dimensional vector space over its kernel. The matrix representation of a spread set for the semifield plane is constructed under the condition that the autotopism group contains a dihedral subgroup of order 8. Using computer technology, we found 34 examples of semifield planes of order 625 with this condition. It is shown also that the autotopism group of a semifield projective plane of order p2n with the kernel of order pn does not contain a subgroup isomorphic to the quaternion group of order 8 when p º1(mod 4).
Журнал: Перспективы развития фундаментальных наук
Выпуск журнала: 3
Номера страниц: 40-42
Место издания: Томск
Издатель: Национальный исследовательский Томский политехнический университет