Counting homomorphisms onto finite solvable groups

2004/05/31 by Daniel Matei, Alexander I. Suciu · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.GR #math.GT #msc:20E07 #msc:20F16 #msc:20F36 #msc:20J05 #msc:57M05

paper · pdf · doi:10.1016/j.jalgebra.2005.01.009

published as Journal of Algebra 286 (2005), 161-186 · 30 pages; accepted for publication in the Journal of Algebra

arxiv created 2005/01/23 · openalex publication_date 2005/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a method for computing the number of epimorphisms from a finitely-presented group G to a finite solvable group Γ, which generalizes a formula of Gäschutz. Key to this approach are the degree 1 and 2 cohomology groups of G, with certain twisted coefficients. As an application, we count low-index subgroups of G. We also investigate the finite solvable quotients of the Baumslag-Solitar groups, the Baumslag parafree groups, and the Artin braid groups.

Citations

• Braids and Permutations

Cited by

• New Permutation Representations of the Braid Group

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