Thompson's group $T$ is $\frac{3}{2}$-generated

Abstract

Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated, and the finite $\frac{3}{2}$-generated groups were recently classified. Turning to infinite groups, in this paper, we prove that the finitely presented simple group $T$ of Thompson is $\frac{3}{2}$-generated. Moreover, we exhibit an element $ζ\in T$ such that for any nontrivial $α\in T$, there exists $γ\in T$ such that $\langle α, ζ^γ\rangle = T$.