Random Generation of Thompson's group $F$

DOI10.1016/J.JALGEBRA.2021.11.024arXiv2011.11862MaRDI QIDQ6354410

Publication date: 22 November 2020

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.

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Probabilistic methods in group theory (20P05)

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