{"paper":{"title":"Nilpotent covers and non-nilpotent subsets of finite groups of Lie type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Azizollah Azad, John R. Britnell, Nick Gill","submitted_at":"2013-05-16T10:22:16Z","abstract_excerpt":"Let $G$ be a finite group, and $c$ an element of $\\mathbb{Z}\\cup \\{\\infty\\}$. A subgroup $H$ of $G$ is said to be {\\it $c$-nilpotent} if it is nilpotent, and has nilpotency class at most $c$. A subset $X$ of $G$ is said to be {\\it non-$c$-nilpotent} if it contains no two elements $x$ and $y$ such that the subgroup $< x,y>$ is $c$-nilpotent. In this paper we study the quantity $\\omega_c(G)$, defined to be the size of the largest non-$c$-nilpotent subset of $L$.\n  In the case that $L$ is a finite group of Lie type, we identify covers of $L$ by $c$-nilpotent subgroups, and we use these covers to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3748","kind":"arxiv","version":3},"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"}