p^m阶阿贝尔p-群同构的判定

Decision of p^m-order Abel p-group Isomorphism

在定理—两阿贝尔p-群同构当且仅当其初等分解列相同的基础上,建立了两pm阶阿贝尔p-群同构的充要条件是其pn(0nm)阶元素的个数相等。

On the basis of theorem that the two Abel p-groups are isomorphic only when if their elementary decomposed columns are identical, the full prerequisite for isomorphism of the two pro-order Abel p-groups is that the numbers of p^m（0 ≤ n ≤ m ）-order elements are equal.