Subgroups of Additive Group of Integers/Examples/Multiples of 4

Example of Subgroup of Additive Group of Integers
Let $4 \Z$ denote the set of integers which are divisible by $4$.

Let $\struct {4 \Z, +}$ be the algebraic structure formed from $4 \Z$ with the operation of integer addition.

Then $\struct {4 \Z, +}$ is a subgroup of the additive group of integers $\struct {\Z, +}$.

Proof
The set of integers which are divisible by $4$ is the underlying set of the additive group of (integer) multiples of $4$.

Thus from Subgroups of Additive Group of Integers, $\struct {4 \Z, +}$ is a subgroup of $\struct {\Z, +}$.