Groups, Geometry, and Dynamics


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Volume 8, Issue 3, 2014, pp. 643–667
DOI: 10.4171/GGD/243

Published online: 2014-10-02

On growth of random groups of intermediate growth

Mustafa G. Benli[1], Rostislav Grigorchuk[2] and Yaroslav Vorobets[3]

(1) Texas A&M University, College Station, USA
(2) Texas A&M University, College Station, United States
(3) Texas A&M University, College Station, USA

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.

Keywords: Group of intermediate growth, space of finitely generated groups, generic property, random group, oscillating growth

Benli Mustafa, Grigorchuk Rostislav, Vorobets Yaroslav: On growth of random groups of intermediate growth. Groups Geom. Dyn. 8 (2014), 643-667. doi: 10.4171/GGD/243