Thompson’s group T is $${3 \over 2}$$-generated

Source abstract

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 $${3 \over 2}$$ 3 2 -generated, and the finite $${3 \over 2}$$ 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 $${3 \over 2}$$ 3 2 -generated. Moreover, we exhibit an element ζ ∈ T such that for any nontrivial α ∈ T , there exists γ ∈ T such that 〈 α , ζ γ 〉 = T .