Left Coset And Right Coset

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Formal Definition

Let H be a subgroup of a group G. The subset $aH=\{ah|h\in H\}$ of G is the left coset of H containing a, while the subset $Ha=\{ha|h\in H\}$ is the right coset of H containing a.

Informal Definition

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Exhibit the left cosets and the right cosets of the subgroup $3\mathbb{Z}$ of $\mathbb{Z}$.

Left cosets:
Right cosets:
Left cosets are same as right cosets because $\mathbb{Z}$ is abelian.


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Additional Comments

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