Year: 2021
Type: preprint
Abstract: Let $n\ge 2$. Let $VB_n$ (resp. $VP_n$) be the virtual braid group (resp. the pure virtual braid group), and let $VT_n$ (resp. $PVT_n$) be the virtual twin group (resp. the pure virtual twin group). Let $Π$ be one of the following quotients: $VB_n/Γ_2(VP_n)$ or $VT_n/Γ_2(PVT_n)$ where $Γ_2(H)$ is the commutator subgroup of $H$. In this paper, we show that $Π$ is a crystallographic group and we characterize the elements of finite order and the conjugacy classes of elements in $Π$. Furthermore, we realize explicitly some Bieberbach groups and infinite virtually cyclic groups in $Π$. Finally, we also study other braid-like groups (welded, unrestricted, flat virtual, flat welded and Gauss virtual braid group) module the respective commutator subgroup in each case.
Source: arXiv (Cornell University)
Institution: Universidade Federal da Bahia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4286910285