{"paper":{"title":"Primitive permutation groups whose subdegrees are bounded above","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Simon M. Smith","submitted_at":"2012-01-04T01:25:08Z","abstract_excerpt":"If $G$ is a group of permutations of a set $\\Omega$ and $\\alpha \\in \\Omega$, then the {\\em $\\alpha$-suborbits} of $G$ are the orbits of the stabilizer $G_\\alpha$ on $\\Omega$. The cardinality of an $\\alpha$-suborbit is called a {\\em subdegree} of $G$. If the only $G$-invariant equivalence classes on $\\Omega$ are the trivial and universal relations, then $G$ is said to be a {\\em primitive} group of permutations of $\\Omega$.\n  In this paper we determine the structure of all primitive permutation groups whose subdegrees are bounded above by a finite cardinal number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0803","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"}