05942236

j

05942236 Tent, Katrin Free polygons, twin trees, and $\mathrm{CAT}(1)$-spaces. Pure Appl. Math. Q. 7, No. 3, 1037-1052 (2011). 2011 International Press, Somerville, MA EN generalized polygons twin trees $\mathrm{CAT}(1)$-spaces Zbl 1010.20017 Generalized polygons with the Moufang property have been classified by {\it J. Tits} and {\it R. M. Weiss} [Moufang polygons. Berlin: Springer (2002; Zbl 1010.20017)]. The goal of the paper under review is to give new constructions of generalized polygons which do not have this Moufang property, but still have a strongly transitive group of automorphisms. These constructions are done through model-theoretic techniques. By taking ultraproducts, the author is able to use these examples to construct new examples of groups acting strongly transitively on twin trees and of a group acting on a $\mathrm{CAT}(1)$ space with some kind of strong transitivity. Jean L\'ecureux (Orsay)