{"paper":{"title":"Finite groups admitting a coprime automorphism satisfying an additional polynomial identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wolfgang Alexander Moens","submitted_at":"2022-02-21T09:58:45Z","abstract_excerpt":"It is known that a finite group with an automorphism $\\varphi$ of coprime order has a soluble radical of $(|\\varphi|,|C_G(\\varphi)|)$-bounded Fitting height and index. We extend this classic result as follows. Let $f(x) = a_0 + a_1 \\cdot x + \\cdots + a_d \\cdot x^d \\in \\mathbb{Z}[x]$ be a primitive polynomial and let $G$ be a finite group with an automorphism $\\varphi$ of coprime order satisfying $ g^{a_0} \\cdot \\varphi(g)^{a_1} \\cdots \\varphi^d(g)^{a_d} = 1 $, for all $g \\in G$. Then the soluble radical of $G$ has $(d,|C_G(\\varphi)|)$-boundex Fitting height and index. The bounds are made expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.10087","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.10087/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}