Unrestricted virtual braids and crystallographic braid groups

Abstract

We show that the crystallographic braid group Bn/[Pn,Pn] embeds naturally in the group of unrestricted virtual braids UVBn, we give new proofs of known results about the torsion elements of Bn/[Pn,Pn], and we characterise the torsion elements of UVBn.

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