Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups

DOI10.1016/j.jpaa.2024.107713zbMATH Open1542.20153MaRDI QIDQ6564631

Pravin Kumar, Tushar Kanta Naik, Neha Nanda, Mahender Singh

Publication date: 1 July 2024

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

Bieberbach groupcrystallographic groupReidemeister-Schreier methodvirtual braid groupvirtual twin groupvirtual triplet group

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Other geometric groups, including crystallographic groups (20H15)

Cites Work

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• A quotient of the Artin braid groups related to crystallographic groups
• Combinatorial properties of virtual braids.
• Bieberbach groups and flat manifolds
• Virtual knot theory
• Real \(K(\pi ,1)\) arrangements from finite root systems
• Automorphisms of odd Coxeter groups
• Virtual and universal braid groups, their quotients and representations
• Linear motion planning with controlled collisions and pure planar braids
• Alexander and Markov theorems for virtual doodles
• The associated Lie algebra of a right-angled Coxeter group
• Structural aspects of twin and pure twin groups
• Commutator subgroups of twin groups and Grothendieck's cartographical groups
• Almost-Bieberbach groups: affine and polynomial structures
• Theory of braids
• Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups
• Doodle groups
• The virtual and universal braids
• Virtual braids
• Planar pure braids on six strands
• Commutator subgroups of virtual and welded braid groups
• ALGEBRAIC EQUATIONS WITH CONTINUOUS COEFFICIENTS AND SOME PROBLEMS OF THE ALGEBRAIC THEORY OF BRAIDS
• Structure and automorphisms of pure virtual twin groups
• Virtual braid groups, virtual twin groups and crystallographic groups
• Congruence subgroups and crystallographic quotients of small Coxeter groups

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