Composite two-generator links

Norwood showed that two-generator knots are prime and provided an example of a composite two-generator link of two components. Here a generalization of a theorem of Norwood shows that certain free products with amalgamation are not generated by any two group elements. This result is used to show that any composite two-generator link has Hopf link summand. The knot summmand is a two-generator knot in which one generator may be chosen to represent the class of a meridian.