Mathematical Sciences: Groups and Rings

这个项目是关于群论和环论的研究。一名调查员将致力于性格理论的研究。特别是，他将研究M-群，可解群的不可约特征标度集的性质，以及这些群中的特征标与素数集之间的相互作用。另一位研究人员将研究群环、交叉积、伽罗瓦理论和包络环。他将Delta方法应用于无限维李代数的限制包络环。他还将确定这种环何时满足多项式恒等式。此外，他还计划研究Grothendieck群和Gelfand-Kirilov维的计算。群是具有一次运算的代数结构。环是具有加法和乘法两种运算的代数结构。它形成一个关于加法的群。这些都是基本的抽象结构，出现在数学、化学和物理的许多环境中。

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.