# Coset facts for kids

If G is a group and H a subgroup of G, x is an element in G, and h is an element in H the **cosets** of H in G are defined as follows:

- Left coset: xH is the set of all the elements h of H multiplied by x on the left.
- Right coset: Hx is the set of all the elements h of H multiplied by x on the right.

When xH = Hx we say that H is normal in G.

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Coset Facts for Kids. *Kiddle Encyclopedia.*