{"paper":{"title":"Engel sinks of fixed points in finite groups","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, Pavel Shumyatsky","submitted_at":"2018-09-08T01:35:33Z","abstract_excerpt":"For an element $g$ of a group $G$, an Engel sink is a subset $\\mathscr{E}(g)$ such that for every $ x\\in G $ all sufficiently long commutators $ [x,g,g,\\ldots,g] $ belong to $\\mathscr{E}(g)$. Let $q$ be a prime, let $m$ be a positive integer and $A$ an elementary abelian group of order $q^2$ acting coprimely on a finite group $G$. We show that if for each nontrivial element $a$ in $ A$ and every element $g\\in C_{G}(a)$ the cardinality of the smallest Engel sink $\\mathscr{E}(g)$ is at most $m$, then the order of $\\gamma_\\infty(G)$ is bounded in terms of $m$ only. Moreover we prove that if for e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02733","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"}