Lifting representations of Z-groups
几何拓扑
2007-05-23 v2 群论
摘要
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.
引用
@article{arxiv.math/0405457,
title = {Lifting representations of Z-groups},
author = {Daniel S. Silver and Susan G. Williams},
journal= {arXiv preprint arXiv:math/0405457},
year = {2007}
}
备注
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 figure