Unrestricted virtual braids and crystallographic braid groups

Abstract

We show that the crystallographic braid group $B_n/[P_n,P_n]$ embeds naturally in the group of unrestricted virtual braids $UV{B}_n$, we give new proofs of known results about the torsion elements of $B_n/[P_n,P_n]$, and we characterise the torsion elements of $UV{B}_n$.