Subgroups of Additive Group of Integers/Examples
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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 $\struct {\Z, +}$.