{"paper":{"title":"Centralizers of coprime automorphisms of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cristina Acciarri, Pavel Shumyatsky","submitted_at":"2011-12-26T18:52:08Z","abstract_excerpt":"Let $A$ be an elementary abelian group of order $p^{k}$ with $k\\geq 3$ acting on a finite $p'$-group $G$. The following results are proved.\n  If $\\gamma_{k-2}(C_{G}(a))$ is nilpotent of class at most $c$ for any $a\\in A^{#}$, then $\\gamma_{k-2}(G)$ is nilpotent and has $\\{c,k,p\\}$-bounded nilpotency class.\n  If, for some integer $d$ such that $2^{d}+2\\leq k$, the $d$th derived group of $C_{G}(a)$ is nilpotent of class at most $c$ for any $a\\in A^{#}$, then the $d$th derived group $G^{(d)}$ is nilpotent and has $\\{c,k,p\\}$-bounded nilpotency class.\n  Earlier this was known only in the case wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5880","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"}