Mathematical Sciences: Groups and Rings

这个项目是关于群论的研究 戒指理论一名调查员将负责调查 理论特别是，他将研究M群， 可解群的不可约特征标度集 以及字符和素数集之间的相互作用， 这些团体。另一个研究员负责研究群环， 交叉积，伽罗瓦理论和包络环。他将 应用Delta方法于无限域的限制包络环 维李代数他还将决定何时这样做， 环满足多项式恒等式。此外，他还计划 工作的计算格罗滕迪克群和Gelfand-Kirilov 维度 群是一个只有一个运算的代数结构。一 环是一个代数结构，有两个运算，加法 和乘法。它在加法方面形成一个群。 这些是基本的抽象结构， 数学、化学和物理的设置。

This project is concerned with research in group theory and ring theory. One investigator will be working on character theory. In particular, he will examine M-groups, the properties of the set of irreducible character degrees of solvable groups and the interactions between characters and sets of primes in these groups. The other investigator will work on group rings, crossed products, Galois theory and enveloping rings. He will apply Delta-methods to restricted enveloping rings of infinite dimensional Lie algebras. He will also determine when such rings satisfy a polynomial identity. Furthermore he plans to work on computations of Grothendieck groups and Gelfand-Kirilov dimension. A group is an algebraic structure with one operation. A ring is an algebraic structure with two operations, addition and multiplication. It forms a group with respect to addition. These are basic abstract structures which occur in many settings in mathematics, chemistry and physics.