# Math Help - cyclic subgroup in free abelian group

1. ## cyclic subgroup in free abelian group

Let $A$ be an abelian group.
We know that all subgroups of $A$ are normal in $A$.

If $A$ is a free abelian group, are cyclic subgroups of $A$ also normal in $A$?

2. I think the answer is yes.

Since free abelian group is also an abelian group, then $bh=hb$ for all $b \in B, h\in $ because $ \leq B$.

So we can get $b^{-1}hb=h \in $.