eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2012-01-01
DMTCS Proceedings vol. AQ,...
Proceedings
10.46298/dmtcs.2991
2991
journal article
Generic properties of random subgroups of a free group for general distributions
Frédérique Bassino
https://orcid.org/0000-0002-0127-9352
Cyril Nicaud
Pascal Weil
We consider a generalization of the uniform word-based distribution for finitely generated subgroups of a free group. In our setting, the number of generators is not fixed, the length of each generator is determined by a random variable with some simple constraints and the distribution of words of a fixed length is specified by a Markov process. We show by probabilistic arguments that under rather relaxed assumptions, the good properties of the uniform word-based distribution are preserved: generically (but maybe not exponentially generically), the tuple we pick is a basis of the subgroup it generates, this subgroup is malnormal and the group presentation defined by this tuple satisfies a small cancellation condition.
https://dmtcs.episciences.org/2991/pdf
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]