Towards a characterization of generalized twisted field planes (Q1347000)

The authors apply a method of \textit{T. Oyama} [Osaka J. Math. 22, 35-54 (1985; Zbl 0561.51006)] to describe quasifields and they show that the (finite) semifields \(f\) can be characterized by special spreads in \(f \oplus f\). With the help of this description they can prove that a semifield plane of order \(q^ 2 = p^{2r}\) with kernel \(\text{GF}(q)\) that admits a collineation whose order is a \(p\)-primitive divisor of \(q^ 2 - 1\) is a generalized twisted field plane. Furthermore, any semifield plane of order \(p^ n\), \(n \geq 3\), \(p^ n \neq 2^ 6\) that admits an autotopism of order \(p^ n - 1\) is desarguesian or a generalized twisted field plane.