Geodesic
Semifield planes admitting the quaternion group $Q_8$
Algebra i logika, Tome 59 (2020) no. 1, pp. 101-115

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We discuss a well-known conjecture that the full automorphism group of a finite projective plane coordinatized by a semifield is solvable. For a semifield plane of order $p^N$ ($p>2$ is a prime, $4\vert p-1$) admitting an autotopism subgroup $H$ isomorphic to the quaternion group $Q_8$, we construct a matrix representation of $H$ and a regular set of the plane. All nonisomorphic semifield planes of orders $5^4$ and $13^4$ admitting $Q_8$ in the autotopism group are pointed out. It is proved that a semifield plane of order $p^4$, $4\vert p-1$, does not admit $SL(2,5)$ in the autotopism group.
Keywords: semifield plane, homology, regular set.
Mots-clés : autotopism group, quaternion group, Baire involution 
@article{AL_2020_59_1_a5,
     author = {O. V. Kravtsova},
     title = {Semifield planes admitting the quaternion group $Q_8$},
     journal = {Algebra i logika},
     pages = {101--115},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_1_a5/}
}
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O. V. Kravtsova. Semifield planes admitting the quaternion group $Q_8$. Algebra i logika, Tome 59 (2020) no. 1, pp. 101-115. http://geodesic.mathdoc.fr/item/AL_2020_59_1_a5/