An affine proof of uniqueness for the smallest generalized quadrangles, including the determination of their automorphism groups

被引：0

作者：

Stroppel, Markus ^{[1
]}

机构：

[1] Univ Stuttgart, Ins Geometrie & Topol, D-70550 Stuttgart, Germany

来源：

NOTE DI MATEMATICA | 2007年 / 27卷 / 01期

关键词：

generalized quadrangle; affine generalized quadrangle; affine derivation; cube; hypercube; automorphism; duality;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show, by elementary means, that any two generalized quadrangles with three points per line and three lines per point are isomorphic. The proof uses affine quadrangles, it also yields that the doily is point-homogeneous, and that its full group of automorphisms is isomorphic to the group of all permutations of a set of order 6. Extending the methods, we treat the case of generalized quadrangles with three points per line (and arbitrary line size) as well.

引用

页码：153 / 169

页数：17