Coset

up:: Group (Mathematics)

Given a group $G$ and an element $g\in G$, the left coset $gG$ is defined as

$$gG=\{gk\mid \forall k\in G\}$$

and the right coset $gG$ is defined as

$$Gg=\{kg\mid \forall k\in G\}$$

In general, left cosets are not equal to right cosets, In fact, we have that A subgroup if normal iff its left cosets equal its right cosets: they are only equal if the subgroup is a Normal Subgroup.

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References

• Coset - Wikipedia