Commutator Subgroups of Singular Braid Groups

The singular braids with n strands, n≥3, were introduced independently by Baez and Birman. It is known that the monoid formed embedded in a group as braid group, denoted SGn. There has been another generalization of groups, GVBn, which was Fang symmetries behind quantum quasi-shuffle structures. GVBn simultaneously generalizes classical well virtual on strands.We investigate commutator subgroups SGn′ GVBn′ these generalized groups. We prove finitely generated if only n≥5, n≥4. Further, we show both are perfect n≥5.