On growth of random groups of intermediate growth

2013/03/06 by Benli, Mustafa G., Grigorchuk, Rostislav, Vorobets, Yaroslav
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1303.1560

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^nα for some α<1.

Related

• Groups of Oscillating Intermediate Growth
• Growth exponent of generic groups
• Universal groups of intermediate growth and their invariant random\n subgroups
• Groups of Intermediate Growth: an Introduction for Beginners
• Growth behaviors in the range e^rα