Random Generation of Thompson's group $F$

Abstract

We prove that under two natural probabilistic models (studied by Cleary, Elder, Rechnitzer and Taback), the probability that a random pair of elements of Thompson's group $F$ generate the entire group is positive. We also prove that for any $k$-generated subgroup $H$ of $F$ which contains a "natural" copy of $F$, the probability of a random $(k+2)$-generated subgroup of $F$ coinciding with $H$ is positive.

15 pages. arXiv admin note: text overlap with arXiv:1611.08264 by other authors

References in corpus (2)

• The generation problem in Thompson group $F$
• On the probability of co-primality of two natural numbers chosen at random (Who was the first to pose and solve this problem?)