{"paper":{"title":"Growth of permutational extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Anna G. Erschler, Laurent Bartholdi","submitted_at":"2010-11-24T01:16:13Z","abstract_excerpt":"We study the geometry of a class of group extensions, containing permutational wreath products, which we call \"permutational extensions\". We construct for all natural number k a torsion group with growth function asymptotically $\\exp(n^{1-(1-\\alpha)^k}),\\quad 2^{3-3/\\alpha}+2^{2-2/\\alpha}+2^{1-1/\\alpha}=2$, and a torsion-free group with growth function asymptotically $\\exp(\\log(n)n^{1-(1-\\alpha)^k})$.\n  These are the first examples of groups of intermediate growth for which the growth function is known.\n  We construct a group of intermediate growth that contains the group of finitely supported"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5266","kind":"arxiv","version":2},"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"}