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 $\hat{I}\P \in T$ such that for any nontrivial $\hat{I}\pm \in T$, there exists ${\hat{I}}^3\in T$ such that $⟨\hat{I}\pm ,\hat{I}{\P }^3⟩=T$.

11 pages; to appear in Israel Journal of Mathematics