{"paper":{"title":"Compact groups all elements of which are almost right Engel","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":"2018-07-14T13:21:24Z","abstract_excerpt":"We say that an element $g$ of a group $G$ is almost right Engel if there is a finite set ${\\mathscr R}(g)$ such that for every $x\\in G$ all sufficiently long commutators $[...[[g,x],x],\\dots ,x]$ belong to ${\\mathscr R}(g)$, that is, for every $x\\in G$ there is a positive integer $n(x,g)$ such that $[...[[g,x],x],\\dots ,x]\\in {\\mathscr R}(g)$ if $x$ is repeated at least $n(x,g)$ times. Thus, $g$ is a right Engel element precisely when we can choose ${\\mathscr R}(g)=\\{ 1\\}$.\n  We prove that if all elements of a compact (Hausdorff) group $G$ are almost right Engel, then $G$ has a finite normal s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06452","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"}