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There has been another generalization of braid groups, denoted by $GVB_n$, $n \\geq 3$, which was introduced by Fang as a group of symmetries behind quantum quasi-shuffle structures. The group $GVB_n$ simultaneously generalizes the classical braid group, as well as the virtual braid group on $n$ strands.\n  We investigate the commutator subgroups $SG_n'$ and $G"},"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":"1806.05902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-15T11:01:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9648bcba0af9fa532a66561071fcdf4afc75aae4f5684f9cde7ef99d110080f1","abstract_canon_sha256":"629de205c5fa07d765b0b89f23dd8a3c66003d114c8695a2c77842ca587d7f62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:58.440599Z","signature_b64":"B20B9m+K59cT8gvy3vJ1KfJOmmH0GoL4my0M0laBntZnxBEev4fGf+4ts5ZNjbVC8ljEQBhpR0futT2AqO4VBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f8f123da77bab8cd0d1f605e4d3885938b8cbd74ed806ce54ab90ec5fac0bb4","last_reissued_at":"2026-05-17T23:55:58.439863Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:58.439863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commutator Subgroups of Singular Braid Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Krishnendu Gongopadhyay, Soumya Dey","submitted_at":"2018-06-15T11:01:30Z","abstract_excerpt":"The singular braids with $n$ strands, $n \\geq 3$, were introduced independently by Baez and Birman. 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