{"paper":{"title":"Subdegree growth rates of infinite primitive permutation groups","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Simon M. Smith","submitted_at":"2006-11-24T14:58:02Z","abstract_excerpt":"A transitive group $G$ of permutations of a set $\\Omega$ is primitive if the only $G$-invariant equivalence relations on $\\Omega$ are the trivial and universal relations.\n  If $\\alpha \\in \\Omega$, then the orbits of the stabiliser $G_\\alpha$ on $\\Omega$ are called the $\\alpha$-suborbits of $G$; when $G$ acts transitively the cardinalities of these $\\alpha$-suborbits are the subdegrees of $G$.\n  If $G$ acts primitively on an infinite set $\\Omega$, and all the suborbits of $G$ are finite, Adeleke and Neumann asked if, after enumerating the subdegrees of $G$ as a non-decreasing sequence $1 = m_0 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611756","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"}