Year: 2004
Type: preprint
Abstract: 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 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.
Source: arXiv (Cornell University)
Authors: Silver, Daniel S., Williams, Susan G.
Institution: University of South Alabama
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950144691