Filling the Nest Gaps

This paper presents a robust construction technique for two-dimensional translation planes of odd order using the notion of nesting previously developed by the authors. More precisely, nonisomorphic planes of orderq2are obtained by constructing replaceable τ-nests for τ roughly between ( )q− √q/2 and ( )q+ √q/2. In all cases the translation complement of any such plane contains a direct product of two cyclic homology groups of order (q+ 1)/2 with affine axes.