{"paper":{"title":"Residual Finiteness Growth in Two-Step Nilpotent Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jonas Der\\'e, Joren Matthys","submitted_at":"2025-05-27T12:17:41Z","abstract_excerpt":"Given a finitely generated residually finite group $G$, the residual finiteness growth $\\text{RF}_G: \\mathbb{N} \\to \\mathbb{N}$ bounds the size of a finite group $Q$ needed to detect an element of norm at most $r$. More specifically, if $g\\in G$ is a non-trivial element with $\\|g\\|_G \\leq r$, so $g$ can be written as a product of at most $r$ generators or their inverses, then we can find a homomorphism $\\phi: G \\to Q$ with $\\phi(g) \\neq e_Q$ and $|Q| \\leq \\text{RF}_G(r)$. The residual finiteness growth is defined as the smallest function with this property. This function has been bounded from "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21090","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21090/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}