Work

Silhouettes and generic properties of subgroups of the modular group

Year: 2025

Type: article

Abstract: We show that the probability for a finitely generated subgroup of the modular group, of size n , to be almost malnormal or non-parabolic, tends to 0 as n tends to infinity – where the notion of the size of a subgroup is based on a natural graph-theoretic representation of the subgroup. The proofs of these results rely on the combinatorial and asymptotic study of a natural map, which associates with any finitely generated subgroup of \mathsf{PSL}_{2}(\mathbb{Z}) a graph which we call its silhouette, which can be interpreted as a conjugacy class of free finite index subgroups of \mathsf{PSL}_{2}(\mathbb{Z}) .

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/897

Authors: Frédérique Bassino, Cyril Nicaud, Pascal Weil

Institutions: Université Sorbonne Paris Nord, Université Gustave Eiffel, Centre National de la Recherche Scientifique

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7081984529

FWCI:

Cites:

Cited by:

Related to: