Additive Group of Integers is Subgroup of Rationals

Theorem
Let $$\left({\mathbb{Z}, +}\right)$$ be the Additive Group of Integers.

Let $$\left({\mathbb{Q}, +}\right)$$ be the Additive Group of Rational Numbers.

Then $$\left({\mathbb{Z}, +}\right)$$ is a normal subgroup of $$\left({\mathbb{Q}, +}\right)$$.