Semisimple torsion in groups of finite Morley rank

Sylow 0-unipotent subgroups in groups of finite Morley rank

One of the central tools in the classification of simple algebraic groups is the distinction between semisimple subgroups and unipotent subgroups. It is not a priori clear how to make this distinction for torsion-free subgroups of a group of finite Morley rank. We exploit the ``graded'' notion of 0-unipotence to develop a Sylow theory for torsion-free subgroups of a solvable group of finite Morley rank. This Sylow theory provides a robust alternative to the usual theory of Carter subgroups, and will be used in the analysis of intersections of Borel subgroups in minimal simple groups.

带挠的Fuchsian群的分类

Classification of Fuchsian groups with torsion

本文证明了有限生成基本群的二维双曲orbifold的等距等价关系是可具体分类的，并利用该结果证明了具有非初等有限生成稳定子的非奇异遍历PSL_2(R)-空间是同质的。

抽象3D-旋转群与二十面体模的识别

Abstract 3D-rotation groups and recognition of icosahedral modules

本文引入了无需向量空间结构的抽象3D-旋转模概念，证明了在不可约假设下仅有Alt(4)、Sym(4)和Alt(5)满足条件，确定了Alt(5)的二十面体模结构，并据此分类了带加性维数的3维无2-挠忠实Alt(5)-模。