Groups, Algorithms and Geometries

Kantor 9731421提出者将研究Lie类型黑盒例外群的快速识别算法(研究始于K.Magaard)，并寻找Lie类型黑盒群的特征(研究始于A.Seress)。这些算法可应用于将所有已知的蒙特卡罗近线性置换群算法升级为拉斯维加斯算法，然后将其版本编程到群论系统的空白中。其他后果将是用于置换群的非常实用的Sylow算法，这也将进入GAP。群论的领域是对称性的数学理论，与许多其他学科相互作用，例如数学之外的物理和化学，数学中的编码论，数论和几何。研究人员的特殊领域是有限群，计算以及在几何和编码中的应用。

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.