{"paper":{"title":"Groups generated by a finite Engel set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Abdollahi, Antonio Tortora, Rolf Brandl","submitted_at":"2011-09-26T04:01:21Z","abstract_excerpt":"A subset $S$ of a group $G$ is called an Engel set if, for all $x,y\\in S$, there is a non-negative integer $n=n(x,y)$ such that $[x,\\,_n y]=1$. In this paper we are interested in finding conditions for a group generated by a finite Engel set to be nilpotent. In particular, we focus our investigation on groups generated by an Engel set of size two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5439","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"}