Spelling theorems and Cohen-Lyndon theorems for one-relator products

DOI10.1016/0022-4049(94)90018-3zbMath0847.20023OpenAlexW2056468103MaRDI QIDQ1321035

James Howie, Andrew J. Duncan

Publication date: 26 May 1994

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

Full work available at URL: https://doi.org/10.1016/0022-4049(94)90018-3

zbMATH Keywords

picturesone-relator productsdouble coset representativesMagnus theoremCohen-Lyndon theoremspelling theorems

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) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items

Structure of words with short 2-length in a free product of groups ⋮ A SPELLING THEOREM FOR TORSION-FREE ONE-RELATOR PRESENTATIONS ⋮ Local quasiconvexity of groups acting on small cancellation complexes. ⋮ On singular equations over torsion-free groups

Cites Work

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• A spelling theorem for staggered generalized 2-complexes, with applications
• A Cohen-Lyndon theorem for free products of locally indicable groups
• The groups \((2,3,p;q)\); asphericity and a conjecture of Coxeter
• A strengthened Freiheitssatz
• The genus problem for one-relator products of locally indicable groups
• The Quotient of a Free Product of Groups by a Single High-Powered Relator. III. The Word Problem
• The nonorientable genus problem for one-relator products
• The Quotient of a Free Product of Groups by a Single High-Powered Relator. II. Fourth Powers
• Knot surgery and primeness
• The Quotient of a Free Product of Groups by a Single High-Powered Relator. I. Pictures. Fifth and Higher Powers
• One-relator quotients of free products
• Weinbaum's Conjecture on Unique Subwords of Nonperiodic Words
• A Magnus theorem for free products of locally indicable groups
• Some results on one-relator groups
• Free Bases for Normal Subgroups of Free Groups