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中文摘要：
在研究一个生成元的自由Abel群上超群结构的基础上，建立了两个生成元的自由Abel群上的超群结构理论，并进行了分析与研究，同时给出了两个生成元的自由Abel群到实数加群的同态方法，并对自由Abel群上的超群结构进行了研究与分类．在此基础上给出了正规超群的分类．证明得出：自由Abel群同构于实数加群及其子群．
英文摘要：
Based on the research of the hypergroup＇s tructure of the free Abelian group with one Generator, this paper creates the theory of the hypergroup＇s structure on the free Abelian group with two Generators, and gives deeply analyse and study. At the same time, this paper gives the homomorphism method from the free Abelian group of two Generators to the real number additive group. More over, this paper studies and classifies the structure of the hypergroup on free Abelian group. In this foundation, this paper makes the method how to classify the normal hypergroup. With strict proof, this paper has drawn an important conclusion that the free Abelian group is isomorphic to the real number additive group and its subgroup.
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