Geodesic
On growth of random groups of intermediate growth
Mustafa G. Benli1 ; Rostislav Grigorchuk2 orcid ; Yaroslav Vorobets1
1Texas A&M University, College Station, USA
2Texas A&M University, College Station, United States
Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 643-667

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DOI

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 enα for some α < 1.
DOI : 10.4171/ggd/243
Classification : 00-XX
Mots-clés : Group of intermediate growth, space of finitely generated groups, generic property, random group, oscillating growth

Mustafa G. Benli  1   ; Rostislav Grigorchuk  2   ; Yaroslav Vorobets  1

1 Texas A&M University, College Station, USA
2 Texas A&M University, College Station, United States 
Mustafa G. Benli; Rostislav Grigorchuk; Yaroslav Vorobets. On growth of random groups of intermediate growth. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 643-667. doi: 10.4171/ggd/243
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     pages = {643--667},
     year = {2014},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/243/}
}
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