On a class of derived translation planes of square order
In earlier papers [Bull. Aust. Math. Soc. 30, 59--66 (1984; Zbl 0549.51002) and Discrete Math. 66, 175--190 (1987; Zbl 0621.51007)] the authors constructed a class of translation planes \(\pi\) of order \(q^2\), where \(q\) is an odd power of a prime such that 5 is a nonsquare in \(\mathrm{GF}(q)\). Now another class of translation planes \(\bar \pi\) is obtained from those planes \(\pi\) by derivation. In fact the planes \(\bar \pi\) turn out to be a class of planes which has been found by \textit{S. Cohen} and \textit{M. J. Ganley} [Q. J. Math. Oxf., II. Ser. 35, 101--113 (1984; Zbl 0541.51005)] by a different approach. A detailed description of the translation complements of the planes \(\bar \pi\) is given. This is used to establish that the classes of planes \(\pi\) and \(\bar \pi\) do not coincide.
scientific article; zbMATH DE number 4101972