Currently I am reading Milnor's paper "Link Groups". In the paper he defines the link group, for every $n$ component link $L$, as a certain quotient of the fundamental group $\pi_1 (S^3 \setminus L)$. On wikipedia in the article titled "link group" one can read that for trivial links this link group is isomorphic to the free group. However I think that this is impossible because the normal closure of the group generated by every meridian is abelian. So are the link groups of the trivial links free?
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