Growth exponent of generic groups

Yann Ollivier (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Grigorchuk and de la Harpe asked if there are many groups with growth exponent close to that of the free group with the same number of generators. We prove that this is in fact the case for a generic group (in the density model of random groups). More generally, we prove that the growth exponent does not change much through a random quotient of a torsion-free hyperbolic group.

Domaines: Théorie des groupes [math.GR]

Yann Ollivier. Growth exponent of generic groups. Commentarii Mathematici Helvetici, 2006, 81, pp.569-593. ⟨hal-00138231⟩