Geodesic
Linear autotopism subgroups of semifield projective planes
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 705-719

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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.
Keywords: semifield plane, homology, Baer involution, Hughes' problem.
Mots-clés : autotopism 
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     title = {Linear autotopism subgroups of semifield projective planes},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Olga V. Kravtsova; Daria S. Skok. Linear autotopism subgroups of semifield projective planes. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 705-719. http://geodesic.mathdoc.fr/item/JSFU_2023_16_6_a0/