Let K be the kernel of an epimorphism G -> Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3 or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group G, then any homomorphism from K onto the symmetric group S-2 (resp. Z(3)) lifts to a homomorphism onto S-3 (resp. alternating group A(4)).
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