On asymptotic densities and generic properties in finitely generated groups
-
Celine Carstensen
,
Benjamin Fine
Abstract
Recall that asymptotic density is a method to compute densities and/or probabilities within infinite finitely generated groups. If 
is a group property, the asymptotic density determines the measure of the set of elements which satisfy . Is this asymptotic density equal to 1, we say that the property is generic in G. is called an asymptotic visible property, if the corresponding asymptotic density is strictly between 0 and 1. If the asymptotic density is 0, then is called negligible. We call a group property suitable if it is preserved under isomorphisms and its asymptotic density exists and is independent of finite generating systems. In this paper we prove that there is an interesting connection between the strong generic free group property of a group G and its subgroups of finite index.
© de Gruyter 2010
Articles in the same Issue
- On asymptotic densities and generic properties in finitely generated groups
- On finite Thurston-type orderings of braid groups
- Subgroup conjugacy problem for Garside subgroups of Garside groups
- The Latin squares and the secret sharing schemes
- A note on the homology of hyperbolic groups
- Cutting up graphs revisited – a short proof of Stallings' structure theorem
- Some geodesic problems in groups
- Search and witness problems in group theory
- Algebraic attacks using SAT-solvers
Articles in the same Issue
- On asymptotic densities and generic properties in finitely generated groups
- On finite Thurston-type orderings of braid groups
- Subgroup conjugacy problem for Garside subgroups of Garside groups
- The Latin squares and the secret sharing schemes
- A note on the homology of hyperbolic groups
- Cutting up graphs revisited – a short proof of Stallings' structure theorem
- Some geodesic problems in groups
- Search and witness problems in group theory
- Algebraic attacks using SAT-solvers
