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

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2025年12月11日

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Collin Bleak,
Scott Harper,
Rachel Skipper

摘要

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 ${3 \over 2}$ $\frac{3}{2}$ -generated, and the finite ${3 \over 2}$ $\frac{3}{2}$ -generated groups were recently classified. Turning to infinite groups, in this paper, we prove that the finitely presented simple group T of Thompson is ${3 \over 2}$ $\frac{3}{2}$ -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.

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

摘要