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

直到最近的“自由”建设的PI和她的合作者，唯一已知的急剧2-和3-传递置换群是那些所产生的线性变换的仿射或射影线。我们将研究这类群体的局限性。寻求急剧2-和3-传递群的正特征不产生线性变换导致我们的伯恩赛德问题，为此，我们提出了一种新的方法，产生更低的指数上的界限无限这样的群体。

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.