## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Parameters of translation generalized quadrangles

Nils Rosehr

#### Abstract

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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 3 (2005), 329-340.

Dates
First available in Project Euclid: 8 September 2005

https://projecteuclid.org/euclid.bbms/1126195338

Digital Object Identifier
doi:10.36045/bbms/1126195338

Mathematical Reviews number (MathSciNet)
MR2173696

Zentralblatt MATH identifier
1102.51004

Subjects
Primary: 51 E 12 51 H 15 20 E 42

#### Citation

Rosehr, Nils. Parameters of translation generalized quadrangles. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 3, 329--340. doi:10.36045/bbms/1126195338. https://projecteuclid.org/euclid.bbms/1126195338