Counting homomorphisms onto finite solvable groups
arXiv:math/0405122 · doi:10.1016/j.jalgebra.2005.01.009
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.
30 pages; accepted for publication in the Journal of Algebra