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CORR
2010
Springer

Statistical properties of subgroups of free groups

8 years 12 months ago
Statistical properties of subgroups of free groups
The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group ar...
Frédérique Bassino, Armando Martino,
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Frédérique Bassino, Armando Martino, Cyril Nicaud, Enric Ventura, Pascal Weil
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