document: On abelian branched coverings of the sphere We obtain an enumeration formula for the number of weak equivalence classes of the branched -LRB- A * B -RRB- - covering of the sphere with m-branch points , when A and B are finite abelian groups with -LRB- | A | , | B | -RRB- = 1 . From this , we can deduce an explicit formula for enumerating the weak equivalence classes of pseudofree spherical -LRB- Zp * Zq -RRB- - actions on a given surface , when p and q are distinct primes
doc_bio_tags: O B I I O O O O O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O B I O O O B I I O B I O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: abelian branched coverings enumeration formula weak equivalence classes finite abelian groups explicit formula pseudofree spherical