Commutator Subgroups of Welded Braid Groups

Let $WB_n$ be the welded (or loop) braid group on n strands, $n \geq 3$. We investigate commutator subgroup of $WB_n$. We prove that the commutator subgroup $WB_n'$ is finitely generated and Hopfian. We show that $WB_n'$ is perfect if and only if $n \geq 5$. We also compute finite presentations for commutator subgroups of flat virtual and flat welded braid groups. Along the way, we investigate adorability of these generalised braid groups.