{"paper":{"title":"On the diameters of McKay graphs for finite simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Aner Shalev, Martin W. Liebeck, Pham Huu Tiep","submitted_at":"2019-11-29T18:36:54Z","abstract_excerpt":"Let $G$ be a finite group, and $\\alpha$ a nontrivial character of $G$. The McKay graph ${\\mathcal M}(G,\\alpha)$ has the irreducible characters of $G$ as vertices, with an edge from $\\chi_1$ to $\\chi_2$ if $\\chi_2$ is a constituent of $\\alpha\\chi_1$. We study the diameters of McKay graphs for simple groups $G$. For $G$ a group of Lie type, we show that for any $\\alpha$, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for $G={\\rm PSL}_n(q)$ or ${\\rm PSU}_n(q)$. We also bound the diameter for symmetric and alternating groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.13284","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/1911.13284/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"}