论文标题
汤普森的组$ t $是$ \ frac {3} {2} $ - 生成
Thompson's group $T$ is $\frac{3}{2}$-generated
论文作者
论文摘要
每个有限的简单组都可以由两个元素生成，实际上，每个非平凡元素都包含在生成对中。具有此属性的组被认为是$ \ frac {3} {2} $ - 生成的，并且最近对有限的$ \ frac {3} {2} $生成的组进行了分类。转向无限的组，在本文中，我们证明了有限的汤普森的简单组$ t $是$ \ frac {3} {2} $ - 生成的。此外，我们在t $中表现出一个元素$ζ\，因此对于任何非平凡的$α\在t $中，存在$γ\ in t $，使得$ \langleα，ζ^γ\ rangle = t $。
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 $\langle α, ζ^γ\rangle = T$.
