Cosets in Abelian Group

Theorem
Let $$G$$ be an abelian group.

Then every right coset modulo $$H$$ is a left coset modulo $$H$$.

That is:
 * $$\forall x \in G: x H = H x$$

In an abelian group, therefore, we can talk about congruence modulo $$H$$ and not worry about whether it's left or right.

Proof
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