Random generation of Thompson group F

Gili Golan Polak

doi:10.1016/j.jalgebra.2021.11.024

Random generation of Thompson group F

Gili Golan Polak

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that under two natural probabilistic models (studied by Cleary, Elder, Rechnitzer and Taback), the probability of a random pair of elements of Thompson group F generating 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.

Original language	American English
Pages (from-to)	507-524
Number of pages	18
Journal	Journal of Algebra
Volume	593
DOIs	https://doi.org/10.1016/j.jalgebra.2021.11.024
State	Published - 1 Mar 2022

Keywords

Random generation
Thompson group F
Tree diagrams

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2021.11.024

Cite this

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title = "Random generation of Thompson group F",

abstract = "We prove that under two natural probabilistic models (studied by Cleary, Elder, Rechnitzer and Taback), the probability of a random pair of elements of Thompson group F generating 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.",

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AB - We prove that under two natural probabilistic models (studied by Cleary, Elder, Rechnitzer and Taback), the probability of a random pair of elements of Thompson group F generating 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.

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KW - Tree diagrams

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DO - 10.1016/j.jalgebra.2021.11.024

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Random generation of Thompson group F

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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