Mathematical Sciences: Research in Finite Group Theory

该奖项支持有限群论领域的研究。首席研究员将研究“不动点”问题，包括算子群不可解的情况。他将研究具有许多正规子群的有限群的特征理论，使用特征分解技术等，将关于任意有限群的问题简化为关于有限（几乎）单群的问题。他还将研究有限几乎单群的理论，扩展和完善他在子群链的最大长度和舒尔指数公式等方面的结果。群是具有单一运算的代数结构。它出现在数学的许多领域，以及物理和化学。有限群的基本组成部分是有限单群。过去十年数学的主要成果之一是有限单群的分类，证明它需要1万到1.5万页的期刊。本研究超越了分类定理，提供了关于有限群的进一步信息。

This award supports research in the area of finite group theory. The principal investigator will study "fixed point" problems, including cases where the operator group is not solvable. He will look into the character theory of finite groups with many normal subgroups, using character factorization techniques among others, to reduce questions about arbitrary finite groups to questions about finite (almost) simple groups. He will also look into the theory of the finite almost simple groups, extending and refining his results on the maximum length of chains of subgroups and Schur index formulas, among others. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as, physics and chemistry. The fundamental building blocks of finite groups are finite simple groups. One of the major results in mathematics of the past decade is the classification of the finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. This research goes beyond the classification theorem to provide further information about finite groups.