Mathematical Sciences: Groups, Algorithms, and Geometries

这项研究涉及概率和 有限群的生成性质特别是 将研究随机置换群的结构。 这些结果将应用于算法问题 关于置换群。主要研究者将 也考虑了仿射函数的有限导数的性质 与p-adic简单群相关联的建筑物。此外，本发明还提供了一种方法， 某些广义四边形之间的关系 将考虑某些平移平面。 群是具有单一运算的代数对象。 本文主要研究确定一个非线性系统的生成元。 从概率的角度来看，有限群。这些问题 直接来自于当代的期望应用 计算机科学

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.