Hyperbolic groups acting sharply 2- or 3-transitively and the Burnside problem (C04)

在PI和她的合作者最近的“自由”构造之前，唯一已知的2-和3-传递置换群是由仿射线或射影线的线性变换产生的。我们将研究这类群体的局限性。对于非线性变换引起的具有明显正特征的2-和3-传递群的探索，使我们得到了Burnside问题，对此，我们提出了一种新的方法，给出了无限个这样的群的指数下界。

Until recent 'free' constructions of the PI and her collaborators, the only known sharply 2- and 3-transitive permutation groups were those arising from linear transformations of the affine or projective line. We will investigate the limitations of this class of groups. The quest for sharply 2- and 3-transitive groups in positive characteristic not arising from linear transformations leads us to the Burnside problem, for which we propose a new approach yielding much lower bounds on the exponent for infinite such groups.