The cyclically presented groups with relators \(x_ix_{i+k}x_{i+l}\).

DOI10.4171/GGD/104zbMath1243.20042OpenAlexW2033259948MaRDI QIDQ531912

Martin Edjvet, Alun G. T. Williams

Publication date: 21 April 2011

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/ggd/104

zbMATH Keywords

finite groupsfree subgroupsasphericityinfinite groupsTits alternativecyclically presented groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Free nonabelian groups (20E05) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items (14)

Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups ⋮ Fractional Fibonacci groups with an odd number of generators ⋮ Hyperbolicity of \(T(6)\) cyclically presented groups ⋮ Fibonacci type presentations and 3-manifolds ⋮ On the Tits alternative for cyclically presented groups with length-four positive relators ⋮ Cyclically presented groups with length four positive relators ⋮ An Investigation Into the Cyclically Presented Groups with Length Three Positive Relators ⋮ Generalized polygons and star graphs of cyclic presentations of groups ⋮ On shift dynamics for cyclically presented groups. ⋮ Redundant relators in cyclic presentations of groups ⋮ GROUPS OF FIBONACCI TYPE REVISITED ⋮ Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups ⋮ On the topology of the groups of type \(\mathfrak{Z}\) ⋮ Isomorphism theorems for classes of cyclically presented groups

Uses Software

• GAP

Cites Work

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• On the T(q)-conditions of small cancellation theory
• Homology of group systems with applications to knot theory
• Families of group presentations related to topology
• LOG groups and cyclically presented groups
• Star Graphs, Projective Planes and Free Subgroups in Small Cancellation Groups
• UNIMODULAR INTEGER CIRCULANTS ASSOCIATED WITH TRINOMIALS
• The aspherical Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups
• Aspherical relative presentations
• TOPOLOGICAL PROPERTIES OF CYCLICALLY PRESENTED GROUPS
• The Schur Multiplicator of Metacyclic Groups

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