# The isomorphism of quotient groups

If $X$ is an abelian group and $A,B$ are its subgroup with $A\cong B$, is quotient group $X/A$ isomorphic to the quotient group $X/B$ ?

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No. There are examples in which $X, A, B$ are all isomorphic to $\mathbb{Z}$. –  Qiaochu Yuan Jul 27 '12 at 3:50
See the answer to this question. –  Zev Chonoles Jul 27 '12 at 3:53