Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$‐generated. Thompson's group $V$ was the first finitely presented infinite simple group to be discovered. The Higman–Thompson groups $V_n$ and the Brin–Thompson groups $mV$ are two families of finitely presented groups that generalise $V$. In this paper, we prove that all of the groups $V_n$, $V_n^{\prime }$ and $mV$ are $\frac{3}{2}$‐generated. As far as the authors are aware, the only previously known examples of infinite noncyclic $\frac{3}{2}$‐generated groups are the pathological Tarski monsters. We conclude with several open questions motivated by our results.

中文翻译：

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无限的32个生成的组

每个有限简单组可以由两个元素生成，Guralnick和Kantor证明，此外，每个非平凡元素都包含在生成对中。具有此属性的组据说是$\frac{3}{2}$生成。汤普森小组$V$是被发现的第一个有限表示的无限简单组。希格曼-汤普森小组$V_{ñ}$ 和布林-汤普森小组 $米V$ 是两个有限表示组的族 $V$。在本文中，我们证明了所有组$V_{ñ}$， $V_{ñ}^{\prime }$ 和 $米V$ 是 $\frac{3}{2}$生成。据作者所知，无限非循环的唯一先前已知的例子$\frac{3}{2}$产生的群体是病理性的塔斯基怪物。最后，我们总结了一些受我们的研究结果启发的开放性问题。