Gröbner-Shirshov bases for extended modular, extended Hecke, and Picard groups.

DOI10.1134/S0001434612110065zbMath1283.20060OpenAlexW1967142574MaRDI QIDQ1946424

Eylem Güzel Karpuz, Ahmet Sinan Cevik

Publication date: 15 April 2013

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434612110065

zbMATH Keywords

word problemPicard groupsGröbner-Shirshov basesextended Hecke groupsextended modular group

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (7)

Gröbner-Shirshov basis and normal forms for the infinite Coxeter group of type \(\widetilde{C}_n\) ⋮ Unnamed Item ⋮ The graph based on Gröbner-Shirshov bases of groups ⋮ GENERALIZED PELL SEQUENCES RELATED TO THE EXTENDED GENERALIZED HECKE GROUPS ${\bar{H}}$ 3,q AND AN APPLICATION TO THE GROUP ${\bar{H}}$ 3,3 ⋮ Gröbner-Shirshov basis for the singular part of the Brauer semigroup ⋮ Gröbner–Shirshov bases and their calculation ⋮ Gröbner–Shirshov bases for congruence classes of complex reflection groups

Cites Work

• Unnamed Item
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• Gröbner-Shirshov bases of some monoids.
• Normal subgroups of Hecke groups \(H(\lambda)\).
• Word problem for Novikov's and Boone's groups via Gröbner-Shirshov bases.
• Gröbner-Shirshov bases for some braid groups.
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• The normal subgroup structure of the extended Hecke groups.
• Gröbner–Shirshov Bases for Schreier Extensions of Groups
• GRÖBNER-SHIRSHOV BASES: SOME NEW RESULTS
• GRÖBNER–SHIRSHOV BASES FOR FREE INVERSE SEMIGROUPS
• Automorphisms and Congruence Subgroups of the Extended Modular Group
• A Two-Generator Presentation for the Picard Group
• The efficiency of standard wreath product
• Gröbner–Shirshov Basis for HNN Extensions of Groups and for the Alternating Group
• Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung

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