Parameters of translation generalized quadrangles
Rosehr, Nils
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 329-340 / Harvested from Project Euclid
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In this note we show that the algebraic parameters of a linear translation generalized quadrangle are not restricted. This is done with a free construction of fourgonal families on vector spaces. Secondly we prove that a compact translation generalized quadrangle can only have the topological parameters $(1,t)$, $(2,2)$, $(3,4t)$ or $(7,8t)$ for $t\in\mathbb N$. This is achieved by determining the possible dimensions of the elements of continuous partial spreads which satisfy a certain planarity condition.
Publié le : 2005-09-14
Classification:  translation generalized quadrangle,  translation group,  free construction,  topological parameters,  spread,  51 E 12,  51 H 15,  20 E 42 
@article{1126195338,
     author = {Rosehr, Nils},
     title = {Parameters of translation generalized quadrangles},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 329-340},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1126195338}
}

Rosehr, Nils. Parameters of translation generalized quadrangles. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  329-340. http://gdmltest.u-ga.fr/item/1126195338/