On growth of random groups of intermediate growth

Benli M. G., Grigorchuk R., Vorobets Y.

GROUPS GEOMETRY AND DYNAMICS, vol.8, no.3, pp.643-667, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.4171/ggd/243
  • Journal Name: GROUPS GEOMETRY AND DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.643-667
  • Keywords: Group of intermediate growth, space of finitely generated groups, generic property, random group, oscillating growth, TORSION, SPACE
  • Middle East Technical University Affiliated: No

Abstract

We study the growth of typical groups from the family of p-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound. At the same time, from a measure-theoretic point of view (i.e., almost surely relative to an appropriately chosen probability measure), the growth function is bounded by e(n alpha) for some alpha < 1.