{"paper":{"title":"On Orbit Equivalence and Permutation groups defined by unordered relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"F. Dalla Volta, J. Siemons","submitted_at":"2010-10-18T09:56:35Z","abstract_excerpt":"For a set $\\Omega$ an unordered relation on $\\Omega$ is a family R of subsets of $\\Omega.$ If R is such a relation we let G(R) be the group of all permutations on $\\Omega$ that preserves R, that is g belongs to G(R) if and only if x in R implies x^{g}\\in R. We are interested in permutation groups which can be represented as G=G(R) for a suitable unordered relation R on $\\Omega.$ When this is the case, we say that G is defined by the relation R, or that G is a relation group. We prove that a primitive permutation group different from the Alternating Group and of degree bigger or equal to 11 is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3536","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"}