|
Geometry-Algebra-Singularities-Combinatorics and Graduate Student |
| Counting Finite Solvable Representations |
| Abstract: For $G$ a finitely presentable group
and $\Gamma$ a finite solvable group we describe a recursive procedure for
computing the number of epimorphisms of $G$ onto $\Gamma$ in terms of cohomological
invariants of $G$ and of the chief series of $\Gamma$. As a corollary we obtain
formulae for the number of index $n$ subgroups of $G$, for low values of
$n$. Finally, we consider applications to solvable representations of knot
groups and other fundamental groups of spaces of the homotopy type
of a $2$-complex. (joint work with Alex Suciu, Northeastern University) |