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The following results are proved.\n  We show that if all elements in $\\gamma_{r-1}(C_G(a))$ are $n$-Engel in $G$ for any $a\\in A^\\#$, then $\\gamma_{r-1}(G)$ is $k$-Engel for some $\\{n,q,r\\}$-bounded number $k$, and if, for some integer $d$ such that $2^d\\leq r-1$, all elements in the $d$th derived group of $C_G(a)$ are $n$-Engel in $G$ for any $a\\in A^\\#$, then the $d$th derived group $G^{(d)}$ is $k$-Engel for some $\\{n,q,r\\}$-bounded number $k$.\n  Assu"},"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":"1707.06889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-07-20T10:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"65727f31961727d2d876104bf71eb9dea9cc6c5268d4bdd819890bc76fecb5d9","abstract_canon_sha256":"dc832f5314e5e4c668f61fb226ad3925465e91145eb95f162051754b0953270a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.241351Z","signature_b64":"cc14Hw94n6qQUZsKx/ZXKUSSzjQZU+6Aa9ntJM7pwCWqPZ8hBjWgYytDuGr51a9usYw/68s4uHeApx5j+QNnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41a2ae0c46ddef8357c310731740ea5a546a07f98f8f8adf39e22e73418c89c3","last_reissued_at":"2026-05-18T00:39:51.240589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.240589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Profinite groups and centralizers of coprime automorphisms whose elements are Engel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cristina Acciarri, Danilo San\\c{c}\\~ao da Silveira","submitted_at":"2017-07-20T10:01:20Z","abstract_excerpt":"Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $r\\geq2$ acting on a finite $q'$-group $G$. The following results are proved.\n  We show that if all elements in $\\gamma_{r-1}(C_G(a))$ are $n$-Engel in $G$ for any $a\\in A^\\#$, then $\\gamma_{r-1}(G)$ is $k$-Engel for some $\\{n,q,r\\}$-bounded number $k$, and if, for some integer $d$ such that $2^d\\leq r-1$, all elements in the $d$th derived group of $C_G(a)$ are $n$-Engel in $G$ for any $a\\in A^\\#$, then the $d$th derived group $G^{(d)}$ is $k$-Engel for some $\\{n,q,r\\}$-bounded number $k$.\n  Assu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06889","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":"1707.06889","created_at":"2026-05-18T00:39:51.240708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06889v1","created_at":"2026-05-18T00:39:51.240708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06889","created_at":"2026-05-18T00:39:51.240708+00:00"},{"alias_kind":"pith_short_12","alias_value":"IGRK4DCG3XXY","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IGRK4DCG3XXYGV6D","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IGRK4DCG","created_at":"2026-05-18T12:31:21.493067+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/IGRK4DCG3XXYGV6DCBZROQHKLJ","json":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ.json","graph_json":"https://pith.science/api/pith-number/IGRK4DCG3XXYGV6DCBZROQHKLJ/graph.json","events_json":"https://pith.science/api/pith-number/IGRK4DCG3XXYGV6DCBZROQHKLJ/events.json","paper":"https://pith.science/paper/IGRK4DCG"},"agent_actions":{"view_html":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ","download_json":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ.json","view_paper":"https://pith.science/paper/IGRK4DCG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06889&json=true","fetch_graph":"https://pith.science/api/pith-number/IGRK4DCG3XXYGV6DCBZROQHKLJ/graph.json","fetch_events":"https://pith.science/api/pith-number/IGRK4DCG3XXYGV6DCBZROQHKLJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ/action/storage_attestation","attest_author":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ/action/author_attestation","sign_citation":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ/action/citation_signature","submit_replication":"https://pith.science/pith/IGRK4DCG3XXYGV6DCBZROQHKLJ/action/replication_record"}},"created_at":"2026-05-18T00:39:51.240708+00:00","updated_at":"2026-05-18T00:39:51.240708+00:00"}