{"paper":{"title":"On the dimension growth of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.GR","authors_text":"Alexander Dranishnikov, Mark Sapir","submitted_at":"2010-08-23T17:39:53Z","abstract_excerpt":"Dimension growth functions of groups have been introduced by Gromov in 1999. We prove that every solvable finitely generated subgroups of the R. Thompson group $F$ has polynomial dimension growth while the group $F$ itself, and some solvable groups of class 3 have exponential dimension growth with exponential control. We describe connections between dimension growth, expansion properties of finite graphs and the Ramsey theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3868","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"}