{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T04:08:26Z","timestamp":1770955706877,"version":"3.50.1"},"reference-count":46,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:p>In this paper, we give a complete characterization of subgroup separability (also known as LERF property) for surface braid groups and virtual (singular) braid groups. More specifically, for a given surface S let [Formula: see text] be the n-string pure braid group of S. We prove that if S is large then [Formula: see text] is not LERF for [Formula: see text]. If S is not large, we prove [Formula: see text] is LERF if and only if S is not the Klein bottle; [Formula: see text] is LERF if and only if S is the disk, sphere or the projective plane; [Formula: see text] is LERF if and only if S is the sphere; and [Formula: see text] is not LERF for every [Formula: see text]. We note these results also hold for the full surface braid groups [Formula: see text], since [Formula: see text] is a finite index subgroup of [Formula: see text]. Finally, we prove that the virtual and virtual singular versions of those groups are LERF if and only if [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0218196726500037","type":"journal-article","created":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T10:13:30Z","timestamp":1761905610000},"page":"173-190","source":"Crossref","is-referenced-by-count":0,"title":["Subgroup separability of surface braid groups and virtual braid groups"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9713-2573","authenticated-orcid":false,"given":"Kisnney","family":"Almeida","sequence":"first","affiliation":[{"name":"Departamento de Ci\u00eancias Exatas, Universidade Estadual de Feira de Santana, Av. 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