Scientific article

Uniform Growth in Groups of Exponential Growth

Published inGeometriae dedicata, vol. 95, no. 1, p. 1-17
Publication date2002

This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free quotients, nonelementary hyperbolic groups, appropriate free products with amalgamation, HNN-extensions and one-relator groups, as well as soluble groups of exponential growth. Several open problems are formulated.

  • Exponential growth
  • Growth of groups
  • Uniform exponential growth
Citation (ISO format)
DE LA HARPE, Pierre. Uniform Growth in Groups of Exponential Growth. In: Geometriae dedicata, 2002, vol. 95, n° 1, p. 1–17.
Main files (1)
Article (Published version)
  • PID : unige:12370
ISSN of the journal0046-5755

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