Thompson’s group T is $${3 \over 2}$$-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 $${3 \over 2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> -generated, and the finite $${3 \over 2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> -generated groups were recently classified. Turning to infinite groups, in this paper, we prove that the finitely presented simple group T of Thompson is $${3 \over 2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> -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 .