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When $C$ is infinite, we show that the Nielsen equivalence classes of the generating $n$-tuples of $G$ correspond bijectively to the orbits of unimodular rows in $M^{n -1}$ under the action of a subgroup of $GL_{n - 1}(R)$. Making no assumption on the cardinality of $C$, we exhibit a comp"},"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":"1604.08896","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-04-29T16:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"3bfdccb2d401561d546373c789d1072599a4113d655ecd4ffba4f2d00b71488b","abstract_canon_sha256":"c44640867d2d903b5fb0942d8e10196840b75cd37f50d30ddd82dc1a80577f44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:40.956149Z","signature_b64":"9LqnZHsOE35PxCBBRgdfbCrGUHnKrl36tnho9szlBVkFXXukVkyyNHP3rWU+bY4vKUpmJ3XMpRGknfILjWjYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9ae293a7ae7c58a85ec7cb9227ac47082efef16a04fb56923b46a325d592237","last_reissued_at":"2026-05-18T00:12:40.955628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:40.955628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generators of split extensions of Abelian groups by cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Luc Guyot","submitted_at":"2016-04-29T16:04:24Z","abstract_excerpt":"Let $G \\simeq M \\rtimes C$ be an $n$-generator group with $M$ Abelian and $C$ cyclic. 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