What is the procedure or to calculate ( or simplify, I'm new in abstract algebra) a quotient group? I know that $A$ a group and $B$ a subgroup we can form the quotient $$A/B $$ for example $$ \mathbb{Z}/n\mathbb{Z} \cong \mathbb{Z_n} $$
but how to know it?
If $B$ is a normal subgroup of $A$, the set for the quotient group $A/B$ consists of cosets of $B$ in $A,$
i.e., {$aB | a\in A$}.
If $B=A$, then this is {$aA|a\in A$}, which is simply {$A$}.
If $B=${$0$}, then this is {$a | a\in A$}, which is simply $A$.
Thus, $A/A$ is a group with one element (i.e., $A$), and $A/${$0$} is isomorphic to $A$.
When $A$ is finite, |$A/B|=|A|/|B|;$
in particular, $|A/A|=|A|/|A|=1$ and $|A/${$0$}$|=|A|/1=|A|$.