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.

中文翻译：

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承认四元数群 Q8 的半场平面

我们讨论了一个众所周知的猜想，即由半场协调的有限射影平面的完全自同构群是可解的。对于 pN 阶半场平面（p > 2 是素数，4|p − 1），允许同构于四元数群 Q8 的自顶置子群 H，我们构造了 H 的矩阵表示和平面的正则集。指出了自拓扑群中所有允许 Q8 的 54 阶和 134 阶非同构半场平面。证明了 p4, 4|p−1 阶半场平面在自拓扑群中不允许 SL(2, 5)。