{"paper":{"title":"Polynomial Bogolyubov for special linear groups via tensor rank","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.RT","math.SP"],"primary_cat":"math.CO","authors_text":"Guy Kindler, Noam Lifshitz, Shai Evra","submitted_at":"2024-03-31T10:52:39Z","abstract_excerpt":"We prove a polynomial Bogolyubov type lemma for the special linear group over finite fields. Specifically, we show that there exists an absolute constant $C>0,$ such that if $A$ is a density $\\alpha$ subset of the special linear group, then the set $AA^{-1}AA^{-1}$ contains a subgroup $H$ of density $\\alpha^C$. Moreover, this subgroup is isomorphic to a special linear group of a smaller rank. We also show that if $A$ is an approximate subgroups then it can be covered by the union of few cosets of $H$. Our proof makes use of the Gurevich--Howe notion of tensor rank, and of a strengthened Bonami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00641","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.00641/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"}