Groups, Algorithms and Geometries

点击翻译按钮获取中文摘要

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.