Short, Highly Imprimitive Words Yield Hyperbolic One-Relator Groups

DOI10.1080/10586458.2021.1982079zbMath1528.20077arXiv2006.15923OpenAlexW3037892671WikidataQ115550157 ScholiaQ115550157MaRDI QIDQ6062279

Christopher H. Cashen, Unnamed Author

Publication date: 30 November 2023

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.15923

zbMATH Keywords

hyperbolic groupBaumslag-Solitar groupsone-relator groupimprimitivity rank

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67) Computational methods for problems pertaining to group theory (20-08)

Related Items

Primitivity rank for random elements in free groups, Uniform negative immersions and the coherence of one-relator groups

Cites Work

• Unnamed Item
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• Primitive words, free factors and measure preservation.
• Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups.
• Small cancellation theory and automatic groups
• A combination theorem for negatively curved groups
• A tighter bound for the number of words of minimum length in an automorphic orbit.
• Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups.
• Topology of finite graphs
• Automorphic orbits in free groups.
• Stallings foldings and subgroups of free groups
• Negative immersions for one-relator groups
• Counting words of minimum length in an automorphic orbit.
• The genus problem for one-relator products of locally indicable groups
• On equivalent sets of elements in a free group
• Virtual geometricity is rare
• Classification of automorphic conjugacy classes in the free group on two generators
• On the hyperbolicity of small cancellation groups and one-relator groups
• The geometry of one-relator groups satisfying a polynomial isoperimetric inequality
• The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces.With the appendix by Khalid Bou–Rabee
• Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility
• Some results on one-relator groups