Isomoprhic and equal symbol for abelian groups Let $A$ and $B$ be two abelian groups and $A$ and $B$ are isomorphic. Moreover suppose that $A$ and $B$ are not the subgroups of the same group. Is it correct to write $A = B$? Thank you.
You should never, ever claim the statement “$A=B$” is true unless $A$ is literally, element-for-element, the same thing as $B$...

... until you are mathematically experienced enough to abuse the notation $=$ responsibly.
It is certainly correct to write $A = B$, in the same way that it is perfectly correct to write $1 = 2$. These are meaningful statements even if they are false.

That said, if you want to assert that $A$ and $B$ are isomorphic, then the standard notations are $A \simeq B$ or $A \stackrel{\sim}{=} B$ and not $A = B$.