{"paper":{"title":"Assouad-Nagata dimension of locally finite groups and asymptotic cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.MG","authors_text":"J.Higes","submitted_at":"2007-11-09T17:52:31Z","abstract_excerpt":"In this work we study two problems about Assouad-Nagata dimension:\n  1) Is there a metric space of non zero Assouad-Nagata dimension such that all of its asymptotic cones are of Assouad-Nagata dimension zero? (Dydak and Higes)\n  2) Suppose $G$ is a locally finite group with a proper left invariant metric $d_G$. If $\\dim_{AN}(G, d_G)>0$, is $\\dim_{AN} (G, d_G)$ infinite? (Brodskiy, Dydak and Lang)\n  The first question is answered positively not only for general metric spaces but also for discrete groups with proper left invariant metrics.\n  The second question has a negative solution. We show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1512","kind":"arxiv","version":3},"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"}