## Bulletin of the Belgian Mathematical Society - Simon Stevin

### A Half 3-Moufang Quadrangle is Moufang

#### Abstract

Recently, we showed that any $3$-Moufang generalized quadrangle is automatically a Moufang quadrangle. In another recent paper, Katrin Tent \cite{Ten:04a} borrowed an argument of the second author to show that the half Moufang condition implies the Moufang condition for generalized quadrangles. In the present paper we show that this argument can be used to further weaken the hypotheses: we define the half $3$-Moufang condition as a kind of greatest common divisor of the $3$-Moufang condition and the half Moufang condition and show that it implies the Moufang condition.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 5 (2006), 805-811.

Dates
First available in Project Euclid: 10 January 2006

https://projecteuclid.org/euclid.bbms/1136902617

Digital Object Identifier
doi:10.36045/bbms/1136902617

Mathematical Reviews number (MathSciNet)
MR2241345

Zentralblatt MATH identifier
1146.51005

Subjects
Primary: 51E12: Generalized quadrangles, generalized polygons

#### Citation

Haot, Fabienne; Van Maldeghem, Hendrik. A Half 3-Moufang Quadrangle is Moufang. Bull. Belg. Math. Soc. Simon Stevin 12 (2006), no. 5, 805--811. doi:10.36045/bbms/1136902617. https://projecteuclid.org/euclid.bbms/1136902617