Davenport Constant Zero-sum Problems

Combinatorial Number Theory was setted up in 1960's, to research the integral sets of defined configuration. This dissertation belongs to additive number problem of Combinatorial Number Theory. It extends the range of unconfirmed group G with D(G), under the basis of Professor Weidong Gao 's study in zero-sum problem on Davenport's constant.Chapter 1 introduces the origin, the history, the development of Combinatorial Number Theory, and some already obtained achievements in this field, primarily expounds zero-sum problem and Davenport's constant for later parts.Chapter 2 is based on the novel mode, property D, which is firstly inducted by Professor Weidong Gao on the research of D(G). Here, we introduce the relationship between property D and D(G). Next, we use E(a) to deeply study property D, and bring out an important result and the proof, namely the equivalence theorem. At the same time we also describe a conjecture on E(a).Chapter 3 aims at the denfinition of E(a), denfined in chapter 2, and mainly analyzes its correlative properties, and makes out a algebraic proof on the conjecture in a small area, which is also a topic.