{"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"}