On some generating set of Thompson's group $F$

TL;DR

This paper proves that Thompson's group F has a special two-element generating set where any two powers of these elements generate a finite index subgroup, revealing new structural properties of the group.

Contribution

It introduces a specific two-element generating set for Thompson's group F with the property that their powers generate finite index subgroups, a novel structural insight.

Findings

Existence of a two-element generating set with special properties

Any two powers of these generators generate finite index subgroups

Advances understanding of the subgroup structure of Thompson's group F

Abstract

We prove that Thompson's group $F$ has a generating set with two elements such that every two powers of them generate a finite index subgroup of $F$.