$\textbf{Quotient group}$
Let $N$ be a normal subgroup of the group $G$. Then the set $G/N=\{gN:g\in G\}$ together with the binary operation $$(aN)\cdot (bN)\coloneqq(ab)N$$ defines a group called the quotient group.
$\textbf{Quotient group}$
Let $N$ be a normal subgroup of the group $G$. Then the set $G/N=\{gN:g\in G\}$ together with the binary operation $$(aN)\cdot (bN)\coloneqq(ab)N$$ defines a group called the quotient group.
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𝐐𝐮𝐨𝐭𝐢𝐞𝐧𝐭 𝐠𝐫𝐨𝐮𝐩
Let 𝑁 be a normal subgroup of the group 𝐺. Then the set 𝐺/𝑁={𝑔𝑁:𝑔∈𝐺} together with the binary operation
(𝑎𝑁)⋅(𝑏𝑁)≔(𝑎𝑏)𝑁
defines a group called the quotient group.