Subgroups of Additive Group of Integers/Examples/Even Integers

Example of Subgroup of Additive Group of Integers
Let $2 \Z$ denote the set of even integers.

Let $\struct {2 \Z, +}$ be the algebraic structure formed from $2 \Z$ with the operation of integer addition.

Then $\struct {2 \Z, +}$ is a subgroup of the additive group of integers $\struct {\Z, +}$.

Proof
The set of even integers is the underlying set of the additive group of (integer) multiples of $2$.

Thus from Subgroups of Additive Group of Integers, $\struct {2 \Z, +}$ is a subgroup of $\struct {\Z, +}$.