Commutator Subgroups of Welded Braid Groups

Soumya Dey; Krishnendu Gongopadhyay

paper

Commutator Subgroups of Welded Braid Groups

arXiv:1704.03897

Abstract

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

arXiv comment15 pages, introduction modified, notations changed, proofs restructured, minor corrections