Nielsen Equivalence in Fuchsian groups with 2-torsion

In this paper we give a complete classification of minimal generating systems in a very general class of Fuchsian groups G. This class includes for example any G with rank(G) greater or equal to 6 and genus(G) equal to 0. Furthermore, the well known problematic case where G has 2-torsion is not excluded. We classify generating systems up to Nielsen equivalence; this notion is strongly related to Heegaard splittings of 3-manifolds. The results of this paper 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.