The Universal Covers of a Family of Extended Generalized Quadrangles
The Universal Covers of a Family of Extended Generalized Quadrangles
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一族扩展广义四边形的全覆盖
DOI：
10.1006/eujc.1998.0241
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Satoshi Yoshiara
中科院分区：
文献类型：
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作者：
Satoshi Yoshiara
给出了（q+1,q?）阶扩展广义四边形Y(S)无穷族的简单连通性的充分条件。1)在给定条件下，由平面族S在pg （5,q）中构造成7。应用此定理，除了q=4外，当S由a (q+1)- arcinpg （3,q）得到时，当S由表6 （p.299}）中显式给出的相关置换多项式的超椭圆构造时，除了可能的Payne类外，Y(S)是单连通的。
A sufficient condition for the simple connectedness is given for an infinite family of extended generalized quadrangles Y(S) of order (q+1,q?1) constructed in 7 from a family S of planes inPG(5,q) with some conditions. Applying this, Y(S) is shown to be simply connected when S is obtained from a (q+1)-arc inPG(3,q) except forq=4, and when S is constructed from the hyperovals for which the associated permutation polynomials are explicitly given in the list 6, p.299}, except possibly for a class of Payne.