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Labru\\`ere and Paris, building on work of Artin, Magnus, Dehn, Nielsen, Lickorish, Zieschang, Birman, Humphries, and others, showed that A(g,p) is generated by a set that is called the ADLH set. We use methods of Zieschang and McCool to give a self-contained, algebraic proof of this result. Labru\\`ere and Paris also"},"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":"1104.5451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-28T17:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"78981388851feb7df0915d0679a1dfc56d16ac0480cc5020c3656c8093a18828","abstract_canon_sha256":"87177f3d96e62916fce4d7372af1c3e6f937a4f01b67dca0b03919aedf175b9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:41.713151Z","signature_b64":"rEqnRcDtNyCUxMT4zNMtgMXRQBsodo5tBPL6OvW/Yblump9rPrvpt9ONA9xigCA+Fk3R+RBYYaBr9mbRgcI2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65130411cef0f91f20d2e79152dad98fe27c854588279ae797f843f26f526327","last_reissued_at":"2026-05-18T04:07:41.712600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:41.712600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Zieschang-McCool method for generating algebraic mapping-class groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Llu\\'is Bacardit, Warren Dicks","submitted_at":"2011-04-28T17:05:35Z","abstract_excerpt":"Let g and p be non-negative integers.\n  Let A(g,p) denote the group consisting of all those automorphisms of the free group on {t_1,...,t_p, x_1,...,x_g, y_1,...y_g} which fix the element t_1t_2...t_p[x_1,y_1]...[x_g,y_g] and permute the set of conjugacy classes {[t_1],....,[t_p]}. Labru\\`ere and Paris, building on work of Artin, Magnus, Dehn, Nielsen, Lickorish, Zieschang, Birman, Humphries, and others, showed that A(g,p) is generated by a set that is called the ADLH set. We use methods of Zieschang and McCool to give a self-contained, algebraic proof of this result. 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