{"paper":{"title":"Quasi-Random profinite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT","math.RT"],"primary_cat":"math.GR","authors_text":"Keivan Mallahi-Karai, Mohammad Bardestani","submitted_at":"2012-02-19T22:31:27Z","abstract_excerpt":"We will investigate quasi-randomness for profinite groups. We will obtain bounds for the mininal degree of non-trivial representations of $\\mathrm{SL}_k(\\mathbb{Z}/(p^n\\mathbb{Z}))$ and $\\mathrm{Sp}_{2k}(\\mathbb{Z}/(p^n\\mathbb{Z}))$. Our method also delivers a lower bound for the minimal degree of a faithful representation for these groups. Using the suitable machinery from functional analysis, we establish exponential lower and upper bounds for the supremal measure of a product-free measurable subset of the profinite groups $\\mathrm{SL}_{k}({\\mathbb{Z}_p})$ and $\\mathrm{Sp}_{2k}(\\mathbb{Z}_p)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4194","kind":"arxiv","version":5},"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"}