The relative hyperbolicity of one-relator relative presentations

DOI10.1515/JGT.2009.025zbMath1219.20030arXiv0807.2487OpenAlexW2165962827MaRDI QIDQ3401168

Le Thi Giang

Publication date: 29 January 2010

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.2487

zbMATH Keywords

word problemrelative presentationsrelatively hyperbolic groupsSQ-universal groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67) Cancellation theory of groups; application of van Kampen diagrams (20F06) Algebraic geometry over groups; equations over groups (20F70)

Related Items (4)

Commutator length of powers in free products of groups ⋮ Curvature distribution, relative presentations and hyperbolicity with an application to Fibonacci groups ⋮ Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator. ⋮ Powers with minimal commutator length in free products of groups

Cites Work

• The SQ-universality and residual properties of relatively hyperbolic groups.
• The Quotient of a Free Product of Groups by a Single High-Powered Relator. III. The Word Problem
• The Kervaire-Laudenbach Conjecture and Presentations of Simple Groups
• Free subgroups of one-relator relative presentations
• The solution of length three equations over groups
• A funny property of sphere and equations over groups
• SOME REMARKS ON ONE-RELATOR AMALGAMATED FREE PRODUCTS II
• Some results on one-relator groups

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