2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71300Let 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 lifts to a homomorphism onto S_3, and any homomorphism from K onto Z_3 lifts to a homomorphism onto the alternating group A_4.Version 2 has a new example 3.6 and other small revisions. To appear in Israel J. Math. Plain TeX, 14 pages with 1 eps figureGeometric TopologyGroup Theory20E07; 37B10; 57M27text