Groups, Algorithms and Geometries

KANTOR 9731421 提出者将研究快速识别算法的黑盒例外群的李型（研究开始与K。Magaard），并找到了Lie型黑盒群的特征（研究始于A.塞雷斯）。 这些应用程序升级所有已知的蒙特卡洛近线性置换群算法的拉斯维加斯算法，其版本将被编程到群论系统GAP。其他结果将是非常实用的Sylow算法的置换群，这也将进入GAP。 群论领域是对称性的数学理论，并与许多其他学科相互作用，例如数学之外的物理和化学，编码理论，数论和数学内部的几何。研究者的特定领域是有限群，计算和应用几何和编码。

KANTOR 9731421 The proposer will investigate fast recognition algorithms for black box exceptional groups of Lie type (research begun with K. Magaard), and finding the characteristic of a black box group of Lie type (research begun with A. Seress). These have applications to upgrading all known Monte Carlo nearly linear permutation group algorithms to Las Vegas algorithms, versions of which will then be programmed into the group theory system GAP. Other consequences will be very practical Sylow algorithms for permutation groups, which will also go into GAP. The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines, for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics.The investigator's particular area is finite groups, computation and applications to geometry and coding.