Definition:Coset Product

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Let $\struct {G, \circ}$ be a group.

Let $N$ be a normal subgroup of $G$.

Let $a, b \in G$.

The coset product of $a \circ N$ and $b \circ N$ is defined as:

$\paren {a \circ N} \circ \paren {b \circ N} = \paren {a \circ b} \circ N$

where $a \circ N$ and $b \circ N$ are the left cosets of $a$ and $b$ by $N$.

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