Direct product of cyclic group of prime-square order and cyclic group of prime-square order

Definition
Let $$p$$ be a prime number. This group is defined in the following equivalent ways:


 * 1) It is the defining ingredient::external direct product of two copies of the defining ingredient::cyclic group of prime-square order, i.e., it is the group $$\mathbb{Z}_{p^2} \times \mathbb{Z}_{p^2}$$.
 * 2) It is the defining ingredient::homocyclic group of order $$p^4$$ and exponent $$p^2$$.