堆垒基问题与零和问题是组合数论的热门研究对象。本项目拟运用有限群的结构、代数、多项式方法、 群环、概率方法和调和分析等工具对有限Abel群上的堆垒问题进行研究。主要内容有：结合多项式方法、群环理论、概率方法与调和分析给出更有效的子集和定理去解决一些经典问题,包括有限Abel群的Olson常数的计算；研究秩不小于3的有限Abel群的零和问题；研究可解群上的零和问题，确定某些可解群的Davenport常数与EGZ常数；用群环理论与抽象代数研究有限Abe群的堆垒基问题。

Additive bases problems and zero-sum problems are popular in Combinatorial Number Theory and their contents are vast. In this project these problems are tackled with many methods, including the structure of finite abelian groups, algebra, polynomial method, group ring, probabilistic method, harmonic analysis and so on. Main contents: combine polynomial method, group ring theory, probabilistic method and harmonic analysis to determine the Olson constant of some special finite abelian groups; study the zero-sum problems of finite abelian groups with rank at least 3; determine the Davenport constant and EGZ constant of some special solvable groups; study the additive bases problems through the group ring theory and the abstract algebra.