Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On asymptotic densities and generic properties in finitely generated groups

On asymptotic densities and generic properties in finitely generated groups 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

On asymptotic densities and generic properties in finitely generated groups

Loading next page...
 
/lp/de-gruyter/on-asymptotic-densities-and-generic-properties-in-finitely-generated-lwtpRngUdS
Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2010.008
Publisher site
See Article on Publisher Site

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.

Journal

Groups - Complexity - Cryptologyde Gruyter

Published: Dec 1, 2010

Keywords: Asymptotic densities; strong generic free group property; braid groups; virtually free groups

There are no references for this article.