Every oriented normal generalized link is the closure of a quasitoric normal generalized braid, and the quasitoric braids form a subgroup.
Bardakov, Paolo Bellingeri, and Celeste Damiani
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Quasitoric representation of generalized braids
Every oriented normal generalized link is the closure of a quasitoric normal generalized braid, and the quasitoric braids form a subgroup.