Quotient map of groups
= Quotient map of groups
{title2=$\pi:G\to G/N,\quad g\mapsto gN$}
The <quotient map of groups> sends each <group element> to its <coset> modulo a <normal subgroup>. It is a <surjective group homomorphism>, with <group kernel> exactly $N$. In the additive six-element example, it sends $0,3$ to $N$, $1,4$ to $1+N$, and $2,5$ to $2+N$. The <quotient map of groups> records the identification that produces the new <group>.