{"paper":{"title":"Autocommuting probability of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Parama Dutta, Rajat Kanti Nath","submitted_at":"2017-02-02T07:35:04Z","abstract_excerpt":"Let $G$ be a finite group and $\\Aut(G)$ the automorphism group of $G$. The autocommuting probability of $G$, denoted by $\\Pr(G, \\Aut(G))$, is the probability that a randomly chosen automorphism of $G$ fixes a randomly chosen element of $G$. In this paper, we study $\\Pr(G, \\Aut(G))$ through a generalization. We obtain a computing formula, several bounds and characterizations of $G$ through $\\Pr(G, \\Aut(G))$. We conclude the paper by showing that the generalized autocommuting probability of $G$ remains unchanged under autoisoclinism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00561","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"}