Dihedral Group of Order 8 in an Autotopism Group of a Semifield Projective Plane of Odd Order


Тип публикации: статья из журнала

Год издания: 2022

Идентификатор DOI: 10.17516/1997-1397-2022-15-3-379-385

Ключевые слова: autotopism, baer involution, homology, semifield plane, spread set

Аннотация: We investigate the well-known hypothesis of D. R. Hughes that the full collineation group of a non-Desarguesian semifield projective plane of a finite order is solvable (the question 11.76 in Kourovka notebook was written down by N. D. Podufalov). The spread set method allows us to prove that any non-Desarguesian semifield plane ofПоказать полностьюorder pN, where p ≡ 1 (mod 4) is prime, does not admit an autotopism subgroup isomorphic to the dihedral group of order 8. As a corollary, we obtain the extensive list of simple non-Abelian groups which cannot be the autotopism subgroups. © Siberian Federal University. All rights reserved.

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Журнал: Journal of Siberian Federal University - Mathematics and Physics

Выпуск журнала: Vol. 15, Is. 3

Номера страниц: 379-385

ISSN журнала: 19971397

Издатель: Siberian Federal University


  • Kravtsova O.V. (Siberian Federal University, Krasnoyarsk, Russian Federation)

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