Strongly Regular (α,β)-Families and Translation Strongly Regular (α,β)-Geometries

强正则(α,β)-族和平移强正则(α,β)-几何(英文)

In this paper, we introduce the concept of a strongly regular (α,β)-family. It gener- alizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular (α,β)-geometries from strongly regular (α,β)-families. Furthermore, we prove that each strongly regular (α,β)-geometry constructed from a strongly regular (α,β)-regulus translation is isomorphic to a translation strongly regular (α,β)-geometry; while t - r > β, the converse is also true.