A Semifield Plane of Odd Order Admitting an Autotopism Subgroup Isomorphic to A5
- Authors: Kravtsova O.V.1, Durakov B.K.1
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Affiliations:
- Siberian Federal University
- Issue: Vol 59, No 2 (2018)
- Pages: 309-322
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171788
- DOI: https://doi.org/10.1134/S0037446618020143
- ID: 171788
Cite item
Abstract
We develop an approach to constructing and classifying semifield projective planes with the use of a spread set. The famous conjecture is discussed on the solvability of the full collineation group of a finite semifield nondesarguesian plane. We construct a matrix representation of a spread set of a semifield plane of odd order admitting an autotopism subgroup isomorphic to the alternating group A5 and find a series of semifield planes of odd order not admitting A5.
Keywords
About the authors
O. V. Kravtsova
Siberian Federal University
Author for correspondence.
Email: ol71@bk.ru
Russian Federation, Krasnoyarsk
B. K. Durakov
Siberian Federal University
Email: ol71@bk.ru
Russian Federation, Krasnoyarsk