{"paper":{"title":"Finite groups with an automorphism of large order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Bors","submitted_at":"2015-09-15T15:40:36Z","abstract_excerpt":"Let $G$ be a finite group, and assume that $G$ has an automorphism of order at least $\\rho|G|$, with $\\rho\\in\\left(0,1\\right)$. Generalizing recent analogous results of the author on finite groups with a large automorphism cycle length, we prove that if $\\rho>1/2$, then $G$ is abelian, and if $\\rho>1/10$, then $G$ is solvable, whereas in general, the assumption implies $[G:\\operatorname{Rad}(G)]\\leq\\rho^{-1.78}$, where $\\operatorname{Rad}(G)$ denotes the solvable radical of $G$. Furthermore, we generalize an example of Horo\\v{s}evski\\u{\\i} to show that in finite groups, the quotient of the max"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04607","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"}