Growth series for the group \(\langle x,y\mid x^{-1}yx=y^ l\rangle\)

DOI10.1007/BF01200431zbMath0820.20036MaRDI QIDQ1842010

C. P. Gill, Donald J. Collins, Martin Edjvet

Publication date: 18 April 1995

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

presentationsgrowth seriesrational functionsfinitely presented groupsrewriting rules

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (19)

Connectedness of spheres in Cayley graphs ⋮ The rationality of Sol-manifolds ⋮ Growth in higher Baumslag-Solitar groups ⋮ Metric properties of Baumslag–Solitar groups ⋮ Conjugation curvature in solvable Baumslag–Solitar groups ⋮ Strict Dead-End Elements in Free Soluble Groups ⋮ On problems related to growth, entropy, and spectrum in group theory ⋮ A context-free and a 1-counter geodesic language for a Baumslag-Solitar group ⋮ Minimal length normal forms for some soluble groups ⋮ Growth in Baumslag–Solitar groups II: The Bass–Serre tree ⋮ Growth in Baumslag–Solitar groups I: subgroups and rationality ⋮ On the dependence of the growth rate on the length of the defining relator ⋮ Negligibity of elliptic elements in ascending HNN-extensions of Zm ⋮ Growth of certain non-positively curved cube groups ⋮ Growth series for the group \(\langle x,y\mid x^{-1}yx=y^ l\rangle\) ⋮ Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles ⋮ GROWTH SERIES OF STEM PRODUCTS OF CYCLIC GROUPS ⋮ A new proof of the growth rate of the solvable Baumslag-Solitar groups ⋮ Rational growth in torus bundle groups of odd trace

Cites Work

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• A geometric approach to the almost convexity and growth of some nilpotent groups
• Growth functions and Euler series
• The combinatorial structure of cocompact discrete hyperbolic groups
• Limitations of the constitutive equation of a simple elastic solid
• Growth functions on Fuchsian groups and the Euler characteristic
• Symmetries of planar growth functions
• Growth series for the group \(\langle x,y\mid x^{-1}yx=y^ l\rangle\)
• A note on curvature and fundamental group
• Forcing in intuitionistic systems without power-set
• Counterexamples Involving Growth Series and Euler Characteristics
• The growth function of a graph group

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