{"paper":{"title":"Orbital graphs of infinite primitive permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Simon M. Smith","submitted_at":"2006-11-24T14:29:28Z","abstract_excerpt":"If $G$ is a group acting on a set $\\Omega$ and $\\alpha, \\beta \\in \\Omega$, the digraph whose vertex set is $\\Omega$ and whose arc set is the orbit $(\\alpha, \\beta)^G$ is called an {\\em orbital digraph} of $G$. Each orbit of the stabiliser $G_\\alpha$ acting on $\\Omega$ is called a {\\it suborbit} of $G$.\n  A digraph is {\\em locally finite} if each vertex is adjacent to at most finitely many other vertices. A locally finite digraph $\\Gamma$ has more than one end if there exists a finite set of vertices $X$ such that the induced digraph $\\Gamma \\setminus X$ contains at least two infinite connected"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611758","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"}