If $A$ is abelian group and $B$ is a subgroup of $A$, $B$ is normal subgroup of $A$.
Is it true that $B \times A/B \cong A$?
I ask because I was watching an online lecture from a course in abstract algebra at Harvard extension school.
And the lecturer (whose name is Peter) was taking about vector spaces and said that if $V$ is a vector space and $W$ is a subspace, then $V/W \times W \cong V$.
So the question which I thought of is: "is this true for all Abelian groups?"
Also, is there a less restricted condition on groups which will make this property hold?