{"paper":{"title":"Groups of given intermediate word growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Anna Erschler, Laurent Bartholdi","submitted_at":"2011-10-17T12:24:38Z","abstract_excerpt":"We show that there exists a finitely generated group of growth ~f for all functions f:\\mathbb{R}\\rightarrow\\mathbb{R} satisfying f(2R) \\leq f(R)^{2} \\leq f(\\eta R) for all R large enough and \\eta\\approx2.4675 the positive root of X^{3}-X^{2}-2X-4. This covers all functions that grow uniformly faster than \\exp(R^{\\log2/\\log\\eta}).\n  We also give a family of self-similar branched groups of growth ~\\exp(R^\\alpha) for a dense set of \\alpha\\in(\\log2/\\log\\eta,1)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3650","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"}