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It has previously been shown that, if $p$ is a prime, $G$ is a cyclic $p$-group and $A$ contains a noncyclic regular subgroup, then the Cayley index of $\\Gamma$ is superexponential in $p$.\n  We present evidence suggesting that cyclic groups are exceptional in this respect. Specifically, we establish the contrasting result that, if $p$ is an odd prime and $G$ is abelian but not cyclic, and has order a power of $p$ at least $p^3$, then there is a Cayley dig"},"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":"1703.02290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-07T09:24:11Z","cross_cats_sorted":[],"title_canon_sha256":"9b88f15af43389f846a1900d053c5e2510d9295251ac3dd885bdb6c9b644312d","abstract_canon_sha256":"31f4d95e2915ba839212e8eeb79c58347ae5c80f27a0bfa0cac5a1b6bb99ac3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:20.281599Z","signature_b64":"7SMsZ3eFFvigeW084+5Xej330UppE5vlJOPSFoZi9wzBJSkfeUgEywgjDVAay2ktEJKgaoaJl09QhsP0uoJxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b98fdc445a5986986a345e571b2e4dad60ac50d5ab53c1ded313da9602c9a098","last_reissued_at":"2026-05-18T00:49:20.281193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:20.281193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gabriel Verret, Joy Morris, Luke Morgan","submitted_at":"2017-03-07T09:24:11Z","abstract_excerpt":"Let $\\Gamma=\\mathrm{Cay}(G,S)$ be a Cayley digraph on a group $G$ and let $A=\\mathrm{Aut}(\\Gamma)$. The Cayley index of $\\Gamma$ is $|A:G|$. It has previously been shown that, if $p$ is a prime, $G$ is a cyclic $p$-group and $A$ contains a noncyclic regular subgroup, then the Cayley index of $\\Gamma$ is superexponential in $p$.\n  We present evidence suggesting that cyclic groups are exceptional in this respect. Specifically, we establish the contrasting result that, if $p$ is an odd prime and $G$ is abelian but not cyclic, and has order a power of $p$ at least $p^3$, then there is a Cayley dig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02290","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.02290","created_at":"2026-05-18T00:49:20.281250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02290v1","created_at":"2026-05-18T00:49:20.281250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02290","created_at":"2026-05-18T00:49:20.281250+00:00"},{"alias_kind":"pith_short_12","alias_value":"XGH5YRC2LGDJ","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XGH5YRC2LGDJQ2RU","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XGH5YRC2","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV","json":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV.json","graph_json":"https://pith.science/api/pith-number/XGH5YRC2LGDJQ2RULZLRWLSNVV/graph.json","events_json":"https://pith.science/api/pith-number/XGH5YRC2LGDJQ2RULZLRWLSNVV/events.json","paper":"https://pith.science/paper/XGH5YRC2"},"agent_actions":{"view_html":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV","download_json":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV.json","view_paper":"https://pith.science/paper/XGH5YRC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02290&json=true","fetch_graph":"https://pith.science/api/pith-number/XGH5YRC2LGDJQ2RULZLRWLSNVV/graph.json","fetch_events":"https://pith.science/api/pith-number/XGH5YRC2LGDJQ2RULZLRWLSNVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV/action/storage_attestation","attest_author":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV/action/author_attestation","sign_citation":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV/action/citation_signature","submit_replication":"https://pith.science/pith/XGH5YRC2LGDJQ2RULZLRWLSNVV/action/replication_record"}},"created_at":"2026-05-18T00:49:20.281250+00:00","updated_at":"2026-05-18T00:49:20.281250+00:00"}