A quotient of the Artin braid groups related to crystallographic groups

DOI10.1016/j.jalgebra.2016.11.003zbMath1367.20034OpenAlexW2550330308MaRDI QIDQ504338

Oscar Ocampo, John Guaschi, Daciberg Lima Gonçalves

Publication date: 16 January 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2016.11.003

zbMATH Keywords

braid groupscrystallographic groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Braid groups; Artin groups (20F36) Other geometric groups, including crystallographic groups (20H15) Engel conditions (20F45)

Related Items

Virtual and universal braid groups, their quotients and representations, Unrestricted virtual braids and crystallographic braid groups, Crystallographic groups and flat manifolds from surface braid groups, Almost-crystallographic subgroups of \(B_n/\Gamma_3(P_n)\) and infra-nilmanifolds with cyclic holonomy, The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient \(B_n/[P_{n},P_{n}\)], Torsion subgroups of quasi-abelianized braid groups, Virtual braid groups, virtual twin groups and crystallographic groups, Congruence subgroups and crystallographic quotients of small Coxeter groups, Almost-crystallographic groups as quotients of Artin braid groups, Embeddings of finite groups in \(B_n/\Gamma_k(P_n)\) for \(k=2,3\), On Bieberbach subgroups of \(B _n/[P _n,P _n\) and flat manifolds with cyclic holonomy \(\mathbb{Z}_{2^d}\)], Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups

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