Geodesic
Dihedral group of order $8$ in an autotopism group of a semifield projective plane of odd order
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 3, pp. 378-384

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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 of order $p^N$, where $p\equiv 1\pmod 4$ 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.
Keywords: semifield plane, spread set, Baer involution, homology
Mots-clés : autotopism. 
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     author = {Olga V. Kravtsova},
     title = {Dihedral group of order $8$ in an autotopism group of a semifield projective plane of odd order},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {378--384},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_3_a10/}
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Olga V. Kravtsova. Dihedral group of order $8$ in an autotopism group of a semifield projective plane of odd order. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 3, pp. 378-384. http://geodesic.mathdoc.fr/item/JSFU_2022_15_3_a10/