{"paper":{"title":"Finite groups with high commuting probability for Sylow subgroups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"D\\'ebora Senise, Eloisa Detomi, Pavel Shumyatsky","submitted_at":"2026-05-21T18:38:01Z","abstract_excerpt":"Given two subsets $X,Y$ of a finite group $G$, we write $\\Pr(X,Y)$ for the probability that random elements $x \\in X$ and $y \\in Y$ commute. If $X,Y$ are subgroups, we denote by $\\Pr^*(X,Y)$ the maximum real number $\\epsilon$ with the property that for every pair of distinct primes $p\\in\\pi(X)$ and $q\\in\\pi(Y)$ there is a Sylow $p$-subgroup $P$ of $X$ and a Sylow $q$-subgroup $Q$ of $Y$ such that $\\Pr(P,Q) \\geq \\epsilon$.\n  In this paper we handle, among other things, finite groups $G$ with high probabilities $\\Pr^*(T,G)$, where $T$ is either a term of the lower central series of $G$ or the ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22955","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/2605.22955/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"}