Gröbner–Shirshov Basis for HNN Extensions of Groups and for the Alternating Group

DOI10.1080/00927870701665180zbMath1206.20028arXiv0804.0642OpenAlexW3101551016MaRDI QIDQ5444889

Chanyan Zhong, Yuqun Chen

Publication date: 26 February 2008

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

Full work available at URL: https://arxiv.org/abs/0804.0642

zbMATH Keywords

HNN extensionsalternating groupsnormal form theoremsGröbner-Shirshov basesShirshov composition lemma

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (12)

Unnamed Item ⋮ Gröbner-Shirshov bases of some Weyl groups ⋮ Gröbner–Shirshov Bases for Schreier Extensions of Groups ⋮ Gröbner-Shirshov bases for extended modular, extended Hecke, and Picard groups. ⋮ The graph based on Gröbner-Shirshov bases of groups ⋮ Gröbner-Shirshov basis for the singular part of the Brauer semigroup ⋮ Gröbner-Shirshov bases of some monoids. ⋮ Gröbner–Shirshov bases and their calculation ⋮ Sufficiency Conditions for Bokut' Normal Forms ⋮ Gröbner-Shirshov Bases of Some Semigroup Constructions ⋮ A solution of the word problem for braid groups via the complex reflection group G12 ⋮ Parametrized Gröbner–Shirshov bases

Cites Work

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• The diamond lemma for ring theory
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• GRÖBNER-SHIRSHOV BASES FOR COXETER GROUPS
• Decision Problems in Group Theory
• Embedding Theorems for Groups

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