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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.06452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-14T13:21:24Z","cross_cats_sorted":[],"title_canon_sha256":"08b1458af6b23f721a4efed81315ee04fab54c6def8f51a13f38a9a0ee5ce0f3","abstract_canon_sha256":"aae6a0752baf2edc4ab913a05f38e2e6d0aaeaf10b4eda0e79f70d1ab611ba59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:32.966771Z","signature_b64":"J4n5VQLWwVaY3K4BTykEJ1v13yXlbcuyhH6Cz9CMeZ1PJfjnp5dfqpXgQ1pkUgqHponLdMAoMzMfhnnPjK2hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1f0cf45ce376ae3096b0228daed88285787c9a394d615b7bf78d3cdbba5ae64","last_reissued_at":"2026-05-18T00:10:32.966072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:32.966072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.06452","created_at":"2026-05-18T00:10:32.966172+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.06452v1","created_at":"2026-05-18T00:10:32.966172+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06452","created_at":"2026-05-18T00:10:32.966172+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HYM6ROOG5VO","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HYM6ROOG5VOGCLL","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HYM6ROO","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB","json":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB.json","graph_json":"https://pith.science/api/pith-number/2HYM6ROOG5VOGCLLAIUNV3MIFB/graph.json","events_json":"https://pith.science/api/pith-number/2HYM6ROOG5VOGCLLAIUNV3MIFB/events.json","paper":"https://pith.science/paper/2HYM6ROO"},"agent_actions":{"view_html":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB","download_json":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB.json","view_paper":"https://pith.science/paper/2HYM6ROO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.06452&json=true","fetch_graph":"https://pith.science/api/pith-number/2HYM6ROOG5VOGCLLAIUNV3MIFB/graph.json","fetch_events":"https://pith.science/api/pith-number/2HYM6ROOG5VOGCLLAIUNV3MIFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB/action/storage_attestation","attest_author":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB/action/author_attestation","sign_citation":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB/action/citation_signature","submit_replication":"https://pith.science/pith/2HYM6ROOG5VOGCLLAIUNV3MIFB/action/replication_record"}},"created_at":"2026-05-18T00:10:32.966172+00:00","updated_at":"2026-05-18T00:10:32.966172+00:00"}