- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2023 16 (6)
- Authors
- Kravtsova, Olga V.; Skok, Daria S.
- Contact information
- Kravtsova, Olga V. : Siberian Federal University Krasnoyarsk, Russian Federation; OCRID: 0000-0002-6005-2393; Skok, Daria S.: Siberian Federal University Krasnoyarsk, Russian Federation;
- Keywords
- semifield plane; autotopism; homology; Baer involution; Hughes’ problem
- Abstract
We investigate the well-known hypothesis of D. R. Hughes that the full collineation group of 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). This hypothesis is reduced to autotopism group that consists of collineations fixing a triangle. We describe the elements of order 4 and dihedral or quaternion subgroups of order 8 in the linear autotopism group when the semifield plane is of rank 2 over its kernel. The main results can be used as technical for the further studies of the subgroups of even order in an autotopism group for a finite non-Desarguesian semifield plane. The results obtained are useful to investigate the semifield planes with the autotopism subgroups from J. G. Thompson’s list of minimal simple groups
- Pages
- 705–719
- EDN
- ARCPOE
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/151860
Journal of Siberian Federal University. Mathematics & Physics / Linear Autotopism Subgroups of Semifield Projective Planes
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