Abstract
A finite group Go, is said to admit a partition if there is a set of subgroups GC, i=1, 2, , s, s_ 2, so that (1) G0=U= Gi and (2) if i j and i, j>0, then GinG,= (e) where e is the identity in Go.2 Such groups are well known.3 The examples considered in this note are abelian groups in which every element has order two, and dihedral groups. Let W be a closed Riemann surface. A conformal self-map of W will be called an automorphism. If G is a finite group of automorphisms of W, then the orbit space, W/G, is naturally a Riemann surface and the natural projection W-*W/G represents W as an n-sheeted covering of W/G where n is the order of G. The formula embodied in the following lemma is followed by some applications. The applications can be considered as generalizations and extensions of the hyperelliptic situation.
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