Mathematical Sciences: Groups, Algorithms, and Geometries

点击翻译按钮获取中文摘要

This research is concerned with probabilistic and generational properties of finite groups. In particular the structure of a random permutation group will be investigated. These results will be applied to algorithmic questions concerning permutation groups. The principal investigator will also consider properties of finite quotients of affine buildings associated with p-adic simple groups. In addition, the relationships among certain generalized quadrangles and certain translation planes will be considered. A group is an algebraic object having a single operation. This work is concerned with determining the generators of a finite group from a probabilistic standpoint. These questions arise directly from desired applications in contemporary computer science.