On growth of random groups of intermediate growth

  • Mustafa G. Benli

    Texas A&M University, College Station, USA
  • Rostislav Grigorchuk

    Texas A&M University, College Station, United States
  • Yaroslav Vorobets

    Texas A&M University, College Station, USA

Abstract

We study the growth of typical groups from the family of -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 for some < 1.

Cite this article

Mustafa G. Benli, Rostislav Grigorchuk, Yaroslav Vorobets, On growth of random groups of intermediate growth. Groups Geom. Dyn. 8 (2014), no. 3, pp. 643–667

DOI 10.4171/GGD/243