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Counting homomorphisms onto finite solvable groups

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: D. Matei, A.I. Suciu

Editorial: Journal of Algebra, 286 (1), p.161-186, 2005.


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 Gaschütz. 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.

Cuvinte cheie: Solvable quotients, chief series, Gaschütz formula, group cohomology, finite-index subgroups, Baumslag-Solitar groups, parafree groups, braid groups