Generic properties of random subgroups of a free group for general distributions
Abstrak
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.
Topik & Kata Kunci
Penulis (3)
Frédérique Bassino
Cyril Nicaud
Pascal Weil
Akses Cepat
- Tahun Terbit
- 2012
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2991
- Akses
- Open Access ✓