We give a complete classification of minimal generating systems in a very general class of Fuchsian groups
. This class includes
for example any
which has at least seven nonconjugate cyclic subgroups of order
.
In particular, the well-known problematic cases where
has characteristic
exponents
are not excluded.
We classify generating systems up to Nielsen equivalence;
this notion is strongly related to Heegaard splittings of
–manifolds.
The results presented here provide in particular the tools for a rather general
extension of previous work of the authors and others on the isotopy classification of
such splittings in Seifert fibered spaces.
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