%0 Journal Article
%T On the semi-direct product structure of CAT(0) groups
%A Tetsuya Hosaka
%J Mathematics
%D 2009
%I arXiv
%X In this paper, we investigate finitely generated groups of isometries of CAT(0) spaces containing some central hyperbolic isometry, and study CAT(0) groups. We show that every CAT(0) group $\Gamma$ has the structure of some semi-direct product $\Gamma = \Gamma' \rtimes B$ where $\Gamma'$ is a CAT(0) group with finite-center and $B$ is a torsion-free Bieberbach group. Also, we introduce an example of a virtually irreducible CAT(0) group with trivial-center that acts geometrically on some CAT(0) space that splits as a product $T \times \R$.
%U http://arxiv.org/abs/0912.0059v4