{"paper":{"title":"Groups acting freely on $\\Lambda$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Myasnikov, D. Serbin, O. Kharlampovich","submitted_at":"2009-11-01T21:34:22Z","abstract_excerpt":"A group is called $\\Lambda$-free if it has a free Lyndon length function in an ordered abelian group $\\Lambda$, which is equivalent to having a free isometric action on a $\\Lambda$-tree. A group has a regular free length function in $\\Lambda$ if and only if it has a free isometric action on a $\\Lambda$-tree so that all branch points belong to the orbit of the base point. In this paper we prove that every finitely presented $\\Lambda$-free group $G$ can be embedded into a finitely presented group with a regular free length function in $\\Lambda$ so that the length function on $G$ is preserved by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0209","kind":"arxiv","version":4},"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"}