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Published online by Cambridge University Press: 09 April 2009
In Neuwirth's book “Knot Groups” ([2]), the structure of the commutator subgroup of a knot is studied and characterized. Later Brown and Crowell refined Neuwith's result ([1], and we thus know that if G is the groups of a knot K, then [G, G] is either free of rank 2g, where g is the genus of K, or a nontrivial free product with amalgamation on a free group of rank 2g, and may be written in the form , where F is free of rank 2g, and the amalgamations are all proper and identical.