On planar functions
Planar functions serve to describe planes of order n admitting a certain type of collineation group of order \(n^ 2\) [cf. \textit{P. Dembowski} and \textit{T. G. Ostrom}; Math. Z. 103, 239-258 (1968; Zbl 0163.424)]. All known examples occur (for odd n) in elementary abelian p-groups and belong to semifield planes. The author gives a general description of such planar functions. He also studies the general case and obtains some non-existence results; e.g., he rules out all orders n of the form \(n=pq\), where p and q are primes for which p divides \(q^ m+1\) for some positive integer m.
scientific article; zbMATH DE number 4150485