{"paper":{"title":"SL(3,Z) is not Howson","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Qiang Zhang, Shengkui Ye","submitted_at":"2026-05-24T13:45:25Z","abstract_excerpt":"We give an explicit construction of two $2$-generated subgroups $H,K\\leq \\SL(3,\\Z)$ whose intersection is not finitely generated. The construction takes place inside the standard parabolic subgroup $\\Z^2\\rtimes \\SL(2,\\Z)\\leq \\SL(3,\\Z)$. The main point is to identify $H\\cap K$ with the stabilizer of a point for an affine action of a free group on $\\Z^2$, and then to prove, using the Schreier graph of this action, that this stabilizer is not finitely generated. Furthermore, we prove that there exists a sequence of subgroups $H_q, K_q \\leq \\SL(3,\\mathbb{Z})$ such that $\\rank(H_q)=\\rank(K_q)=4$, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25080","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/2605.25080/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"}