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 ...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.展开更多
基金the Scientific Research Start-Up Foundation of Qingdao University of Science and Technology in China. (No.0022327)
文摘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.
