cyclic subgroup in free abelian group

**deniselim17** · July 25th 2009, 10:32 PM

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 $A$ ?

**deniselim17** · July 25th 2009, 10:43 PM

I think the answer is yes.

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

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

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