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 pN (p > 2 is a prime, 4|p − 1) admitting an autotopism subgroup H isomorphic to the quaternion group Q8, we construct a matrix representation of H and a regular set of the plane. All nonisomorphic semifield planes of orders 54 and 134 admitting Q8 in the autotopism group are pointed out. It is proved that a semifield plane of order p4, 4|p−1, does not admit SL(2, 5) in the autotopism group.
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Supported by RFBR, project No. 19-01-00566 a.
Translated from Algebra i Logika, Vol. 59, No. 1, pp. 101-115, January-February, 2020.
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Kravtsova, O.V. Semifield Planes Admitting the Quaternion Group Q8. Algebra Logic 59, 71–81 (2020). https://doi.org/10.1007/s10469-020-09583-y
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DOI: https://doi.org/10.1007/s10469-020-09583-y