当2<β<q时全嵌入在AG(3,q)中的(1,β)-几何

(1,β)-geometries Fullly Embedded in AG(3,q) with 2<β<q

(α,β)-几何是有限几何中一类重要的关联结构。讨论了(1,β)-几何在AG(3,q)中的全嵌入。证明了如果2<β<q,S=(P,L,I)是一个全嵌入在AG(3,q)中的(1,β)-几何,那么当β(β-1)>q且t>q时,S是一个线性表示。

（α ,β）-geometries are a class of important incidence structures in finite geometry. The （1 ,β）-geometries fully embedded is studied in AG（3 ,q）. If 2 〈β 〈q,S = （P,L,I） is a （1 ,β）-geometry fully embedded in AG （3 ,q）Which is proved,then S is a linear linear representation whenβ（β -1 ） 〉 q and t 〉 q.