{"paper":{"title":"Normal coverings of linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Maroti, John R. Britnell","submitted_at":"2012-06-19T17:49:11Z","abstract_excerpt":"For a non-cyclic finite group $G$, let $\\gamma(G)$ denote the smallest number of conjugacy classes of proper subgroups of $G$ needed to cover $G$. Bubboloni, Praeger and Spiga, motivated by questions in number theory, have recently established that $\\gamma(S_n)$ and $\\gamma(A_{n})$ are bounded above and below by linear functions of $n$. In this paper we show that if $G$ is in the range $\\SL_{n}(q)\\le G\\le \\GL_{n}(q)$ for $n>2$, then $n/\\pi^2 < \\gamma(G) \\le (n+1)/2$. We give various alternative bounds, and derive explicit formulas for $\\gamma(G)$ in some cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4279","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":""},"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"}