2020/09/07 by Nguyen, Hoang Thanh, Yang, Wenyuan · 1 citation
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2009.02863
Croke-Kleiner admissible groups firstly introduced by Croke-Kleiner belong to a particular class of graph of groups which generalize fundamental groups of 3--dimensional graph manifolds. In this paper, we show that if G is a Croke-Kleiner admissible group, acting geometrically on a CAT(0) space X, then a finitely generated subgroup of G has finite height if and only if it is strongly quasi-convex. We also show that if G \curvearrowright X is a flip CKA action then G is quasi-isometric embedded into a finite product of quasi-trees. With further assumption on the vertex groups of the flip CKA action G \curvearrowright X, we show that G satisfies property (QT) that is introduced by Bestvina-Bromberg-Fujiwara.