Direct product of Z4 and Z4

Definition
This group, denoted $$\mathbb{Z}_4 \times \mathbb{Z}_4$$ or $$C_4 \times C_4$$ is defined in the following equivalent ways:


 * It is a homocyclic group of order sixteen and exponent four.
 * It is the direct product of two copies of cyclic group:Z4.

As an abelian group of prime power order
This group is the abelian group of prime power order corresponding to the partition:

$$\! 4 = 2 + 2$$

In other words, it is the group $$\mathbb{Z}_{p^2} \times \mathbb{Z}_{p^2}$$.

Other descriptions
The group can also be defined using GAP's DirectProduct function:

DirectProduct(CyclicGroup(4),CyclicGroup(4))