将无穷群加以分类，定义了一致幂群的概念，并研究了一致幂群的运算性质。
In this article, the hypergroups of infinite group are classified, and the uniform hypergroup is defined and its operation properties are also discussed.
通过引入广义核概念，详细讨论了各类幂群的结构，并给出了一类幂群的构造定。
The stractures of power groups are discussed systematically by introducing generalized kernel and the constructivity theorem on a class of power group is established.
利用群作用给出了一经线性 （无限 ）群在无限幂群上的作用 ，利用这一作用定义了无限幂群的正则表示和相应的矩阵表示 。
In this paper, the regular representations and matrix representations of an infinite powergroups are given by the infinite linear group actions on the infinite powergroup.
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