The nonorientable genus problem for one-relator products

DOI10.1080/00927879108824278zbMath0731.20022OpenAlexW1977775387MaRDI QIDQ3356523

Andrew J. Duncan, James Howie

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1080/00927879108824278

zbMATH Keywords

wordsgeneratorsone-relator productsdecision problemrecursive presentationgenus problemword and conjugacy problemslocally indicablepictures over presentations

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Fundamental group, presentations, free differential calculus (57M05) 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) Local properties of groups (20E25) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items

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

Cites Work

• Quadratic equations over free groups and free products
• Using surfaces to solve equations in free groups
• Surfaces in three-manifolds and non-singular equations in groups
• Applications of topological graph theory to group theory
• The genus problem for one-relator products of locally indicable groups
• Star-complexes, and the dependence problems for hyperbolic complexes