A new generalization of Moulton affine planes
Following \textit{W. A. Pierce} [Can. J. Math. 13, 427-436 (1961; Zbl 0103.134)], the author considers a variation on his construction of Moulton planes. However he takes a different view and describes lines of negative slope by equations \(g(y)=mf(x)+n\) and remaining lines by equations \(x=c\) or \(y=mx+n\) with \(m=0\). In Section 1 he investigates under what conditions on \(f\) and \(g\) we obtain an affine plane, in Section 2 he considers some special cases, including the case of finite fields. The questions are whether his construction really yields new planes not isomorphic to already known planes and under what conditions are the planes constructed in his article isomorphic to each other. At present the author does not know the answers but in Section 3 he describes some examples to give some idea of what is to be expected.
scientific article; zbMATH DE number 58792
scientific article