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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1010.3536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-18T09:56:35Z","cross_cats_sorted":[],"title_canon_sha256":"f909e7f351eb8a9329f97d88ed27c52a89e9b3a48c557492585fe8f691223ec5","abstract_canon_sha256":"dbe0ae1b3f34e96fd80c3fd0a8326a89c2cecf42fb8297ead47759b6008ee732"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:08.869077Z","signature_b64":"jsep7bKS9J+mC+UxqVqj/3L5GGEz2q+S84N1yNHNl6K3xRiluXLzrDFKcWtPihZZykXKElIdYPkK1zZ6slDbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18b2dd0cc0b8acb8e10063e4211f8bbb9f234a5d533edf6c74c4d9e2e20fce37","last_reissued_at":"2026-05-18T04:39:08.868607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:08.868607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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