Mathematical Sciences: Groups, Algorithms, and Geometries

本研究涉及有限群的概率性和世代性。特别地，随机置换群的结构将被研究。这些结果将应用于关于置换群的算法问题。首席研究员还将考虑与p进单群相关的仿射建筑物的有限商的性质。此外，还将考虑某些广义四边形与某些平移平面之间的关系。群是具有单一运算的代数对象。本文从概率的角度研究有限群的产生子。这些问题直接来自于当代计算机科学的应用。

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.