{"paper":{"title":"Forbidden relations in universal virtual braid groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Charalampos Stylianakis, Oscar Ocampo","submitted_at":"2026-06-04T12:32:53Z","abstract_excerpt":"We study natural automorphisms of the universal virtual braid group $UV_n(k)$. These automorphisms induce commuting involutions in the outer automorphism group and generate a subgroup isomorphic to $\\mathbb{Z}_2^k\\times\\mathbb{Z}_2$. We then show that the two one-forbidden quotients of $UV_n(k)$ are isomorphic. Furthermore, we introduce the universal unrestricted virtual braid group $UUV_n(k)$ obtained by imposing simultaneously the two forbidden relations, and derive several structural properties inherited from the universal setting. Since the multi-virtual braid group $M_kVB_n$ is a quotient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06095","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06095/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}