Counting homomorphisms onto finite solvable groups

Details Counting homomorphisms onto finite solvable groups Counting homomorphisms onto finite solvable groups

2004-05-07

arxiv.org/abs/math/0405122v3

Journal of Algebra 286 (2005), 161-186

Mathematics

Group Theory

30 pages; accepted for publication in the Journal of Algebra

Scientific paper

10.1016/j.jalgebra.2005.01.009

We present a method for computing the number of epimorphisms from a finitely-presented group G to a finite solvable group \Gamma, which generalizes a formula of G\"aschutz. 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.

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