{"paper":{"title":"Primitive groups and synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Artur Schaefer, Gordon Royle, Jo\\~ao Ara\\'ujo, Peter J. Cameron, Wolfram Bentz","submitted_at":"2015-04-07T14:59:30Z","abstract_excerpt":"Let $\\Omega$ be a set of cardinality $n$, $G$ a permutation group on $\\Omega$, and $f:\\Omega\\to\\Omega$ a map which is not a permutation. We say that $G$ \\emph{synchronizes} $f$ if the transformation semigroup $\\langle G,f\\rangle$ contains a constant map, and that $G$ is a \\emph{synchronizing group} if $G$ synchronizes \\emph{every} non-permutation.\n  A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every non-synchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01629","kind":"arxiv","version":3},"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"}