{"paper":{"title":"On the semi-direct product structure of CAT(0) groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Tetsuya Hosaka","submitted_at":"2009-12-01T03:03:48Z","abstract_excerpt":"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 semi-direct product structure $\\Gamma=(\\cdots(((\\Gamma'\\rtimes\\langle\\delta_{n}\\rangle)\\rtimes\\langle\\delta_{n-1}\\rangle)\\rtimes\\langle\\delta_{n-2}\\rangle)\\cdots)\\rtimes\\langle\\delta_{1}\\rangle$ where $\\Gamma'$ is a CAT(0) group with finite center and $\\delta_i\\in \\Gamma$ for $i=1,\\dots,n$, and $\\Gamma$ contains a finite-index subgroup $\\Gamma'\\times A$ where $A$ is isomorphic to ${\\mathbb{Z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0059","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}