{"paper":{"title":"Orbit coherence in permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"John R. Britnell, Mark Wildon","submitted_at":"2012-05-22T16:13:34Z","abstract_excerpt":"This paper introduces the notion of orbit coherence in a permutation group. Let $G$ be a group of permutations of a set $\\Omega$. Let $\\pi(G)$ be the set of partitions of $\\Omega$ which arise as the orbit partition of an element of $G$. The set of partitions of $\\Omega$ is naturally ordered by refinement, and admits join and meet operations. We say that $G$ is join-coherent if $\\pi(G)$ is join-closed, and meet-coherent if $\\pi(G)$ is meet-closed.\n  Our central theorem states that the centralizer in $\\Sym(\\Omega)$ of any permutation $g$ is meet-coherent, and subject to a certain finiteness cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4960","kind":"arxiv","version":2},"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"}