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Lifting representations of ℤ-groups

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Abstract

LetK be the kernel of an epimorphismG→ℤ, whereG is a finitely presented group. IfK has infinitely many subgroups of index 2,3 or 4, then it has uncountably many. Moreover, ifK is the commutator subgroup of a classical knot groupG, then any homomorphism fromK onto the symmetric groupS 2 (resp. ℤ3) lifts to a homomorphism ontoS 3 (resp. alternating groupA 4).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Alabama, 36688, Mobile, AL, USA

    Daniel S. Silver & Susan G. Williams

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  1. Daniel S. Silver
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  2. Susan G. Williams
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Correspondence to Daniel S. Silver.

Additional information

Both authors partially supported by NSF grants DMS-0071004 and DMS-0304971.

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Silver, D.S., Williams, S.G. Lifting representations of ℤ-groups. Isr. J. Math. 152, 313–331 (2006). https://doi.org/10.1007/BF02771989

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  • DOI: https://doi.org/10.1007/BF02771989

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