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Groups, Geometry, and Dynamics

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Volume 7, Issue 3, 2013, pp. 535–541
DOI: 10.4171/GGD/195

Published online: 2013-08-27

Regular elements in CAT(0) groups

Pierre-Emmanuel Caprace[1] and Gašper Zadnik[2]

(1) Université Catholique de Louvain, Belgium
(2) University of Ljubljana, Slovenia

Let $X$ be a locally compact geodesically complete $\mathrm{CAT}(0)$ space and $\Gamma$ be a discrete group acting properly and cocompactly on $X$. We show that $\Gamma$ contains an element acting as a hyperbolic isometry on each indecomposable de Rham factor of $X$. It follows that if $X$ is a product of $d$ factors, then $\Gamma$ contains $\mathbb{Z}^d$.

Keywords: CAT(0) group, regular elements, flat closing conjecture

Caprace Pierre-Emmanuel, Zadnik Gašper: Regular elements in CAT(0) groups. Groups Geom. Dyn. 7 (2013), 535-541. doi: 10.4171/GGD/195