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Math Help - cyclic subgroup in free abelian group

  1. #1
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    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?
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  2. #2
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    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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