On Fuchsian groups with the same set of fixed points of parabolic elements. (English) Zbl 1188.30051
It is known that two arithmetic Fuchsian groups with the same set of axes of hyperbolic elements are necessarily commensurable. Similarly, the author proves that two arithmetic Fuchsian groups containing parabolic elements and having the same set of fixed points of parabolic elements are necessarily commensurable. This result does not extend to arbitrary cofinite Fuchsian groups.
Reviewer: Jürgen Elstrodt (Münster)
MSC:
| 30F35 | Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) |
| 20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
| 11F06 | Structure of modular groups and generalizations; arithmetic groups |
| 30F40 | Kleinian groups (aspects of compact Riemann surfaces and uniformization) |
