Subgroups of Additive Group of Integers/Examples

Examples of Subgroups of Additive Group of Integers

Even 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 $\struct {\Z, +}$.

Multiples of $4$

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 $\struct {\Z, +}$.