A class of non-ordinary half-planes (Q911048)

A set G of permutations on E is called 2-homogeneous if it acts regular on the 2-subsets of E; G is termed planar by the author if it can be partitioned into subsets M of G which act regular on points and \(\forall \alpha \in M\) \(\forall \beta \in G\setminus M\) \(\exists x\in E:\) \(\alpha (x)=\beta (x)\). Non-planarity is shown for some G contained in the group of affine transformations of certain non-planar nearfields or quasifields. Such G yield examples of non-ordinary half planes, thus answering a question from \textit{D. G. Glynn} [Ars Comb. 19A, 309-342 (1985; Zbl 0561.51013)].