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Equivalently, $G$ has two generating triples of type $(2,3,7)$, such that no generator in one triple is conjugate to a power of a generator in the other. We show that this property is satisfied by alternating groups $A_n$, their double covers $2.A_n$, and special linear groups $SL_n(q)$ if $n$ is sufficiently large, but by no sporadic s"},"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":"1709.09441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-27T10:42:15Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"5955119fd406588f54cf35d2b8597979e526ace21fe226809ce72b58182d9894","abstract_canon_sha256":"66a4c4d56c44d17c17200f0d8206e09e1b94cc2a93fad6e6f36ff6c7629247b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:11.731627Z","signature_b64":"NhZDESAzQyX/R4xlEbvlNRhEyV5uV9nH1bdVerg0ugaAhzPy6PvC9FcoCtonynka103pnpKrSOXJLMJowOO3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae7996aa38afb0a4170162ead367c3e85d8bce48a0d4145456c874343796f2e8","last_reissued_at":"2026-05-18T00:34:11.731061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:11.731061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Doubly Hurwitz Beauville groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.GR","authors_text":"Emilio Pierro, Gareth A. 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