Abelian group of prime power order

Definition
An abelian group of prime power order is a group of prime power order that is also an abelian group.

Classification
As a particular case of the structure theorem for finitely generated abelian groups, we can say the following. For a prime $$p$$ and a nonnegative integer $$n$$, the abelian groups of order $$p^n$$ correspond to unordered integer partitions of $$n$$. Specifically, a partition $$n = k_1 + k_2 + \dots + k_r$$ corresponds to the group:

$$\! \prod_{i=1}^r \mathbb{Z}/p_i^{k_i}\mathbb{Z}$$