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

急剧作用 2- 或 3- 传递的双曲群以及 Burnside 问题 (C04)

• 批准号: 444034621
• 金额: --
• 依托单位: Institut für Mathematische Logik und Grundlagenforschung
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/444034621?language=en
• 关键词: Hyperbolic; groups; acting; sharply; transitively

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.

直到最近 PI 及其合作者的“自由”构造为止，唯一已知的尖锐 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置换群。我们将研究此类群体的局限性。对不是由线性变换产生的正特性的尖锐 2- 和 3- 传递群的追求将我们引向伯恩赛德问题，为此我们提出了一种新方法，为无限此类群的指数产生低得多的界限。