{"paper":{"title":"On subgroups of Brin-Thompson groups $nV$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Brin-Thompson group nV is torsion locally finite for all n at least 1, and for n at least 2 it contains infinite-order elements that admit roots of arbitrarily large order.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Sadayoshi Kojima, Xiaobing Sheng","submitted_at":"2026-03-19T02:18:09Z","abstract_excerpt":"We prove that the Brin-Thompson group $nV$ is torsion locally finite for $ n \\geq 1$ which is known only when $n = 1$, and $nV$ contains continuum many copies of the additive group of the rationals $\\mathbb{Q}$ for $n \\geq 2$ which is known to be false for the $n = 1$ case."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the Brin-Thompson group nV is torsion locally finite for n ≥ 1 which is known only when n = 1, and nV contains elements of infinite order admitting roots with arbitrary large order for n ≥ 2 which is known to not be true for the n = 1 case.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proofs rely on the standard combinatorial definition and known properties of Brin-Thompson groups nV for n=1, together with the generalization to higher n; without the full manuscript the precise steps and any hidden assumptions in the extension cannot be checked.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"nV is torsion locally finite for all n≥1 and for n≥2 contains infinite-order elements admitting roots of arbitrarily large order.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Brin-Thompson group nV is torsion locally finite for all n at least 1, and for n at least 2 it contains infinite-order elements that admit roots of arbitrarily large order.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7b97ead796dda3bd3306652411ae0c774d2d34cb0546dbe689e237e1ec40d3b6"},"source":{"id":"2603.18410","kind":"arxiv","version":3},"verdict":{"id":"eb743637-46a8-4840-8231-8b278e528799","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T09:11:03.853909Z","strongest_claim":"We prove that the Brin-Thompson group nV is torsion locally finite for n ≥ 1 which is known only when n = 1, and nV contains elements of infinite order admitting roots with arbitrary large order for n ≥ 2 which is known to not be true for the n = 1 case.","one_line_summary":"nV is torsion locally finite for all n≥1 and for n≥2 contains infinite-order elements admitting roots of arbitrarily large order.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proofs rely on the standard combinatorial definition and known properties of Brin-Thompson groups nV for n=1, together with the generalization to higher n; without the full manuscript the precise steps and any hidden assumptions in the extension cannot be checked.","pith_extraction_headline":"The Brin-Thompson group nV is torsion locally finite for all n at least 1, and for n at least 2 it contains infinite-order elements that admit roots of arbitrarily large order."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.18410/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":2,"snapshot_sha256":"acd80d5a4796ffd322a9c01ee798be0a5d42a1a2320b6e5f07ec13625f4dbae4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}