{"paper":{"title":"Almost Engel compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"E. I. Khukhro, P. Shumyatsky","submitted_at":"2016-10-06T21:44:54Z","abstract_excerpt":"We say that a group $G$ is almost Engel if for every $g\\in G$ there is a finite set ${\\mathscr E}(g)$ such that for every $x\\in G$ all sufficiently long commutators $[...[[x,g],g],\\dots ,g]$ belong to ${\\mathscr E}(g)$, that is, for every $x\\in G$ there is a positive integer $n(x,g)$ such that $[...[[x,g],g],\\dots ,g]\\in {\\mathscr E}(g)$ if $g$ is repeated at least $n(x,g)$ times. (Thus, Engel groups are precisely the almost Engel groups for which we can choose ${\\mathscr E}(g)=\\{ 1\\}$ for all $g\\in G$.)\n  We prove that if a compact (Hausdorff) group $G$ is almost Engel, then $G$ has a finite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02079","kind":"arxiv","version":2},"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"}