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Published online by Cambridge University Press: 18 May 2009
Let G be a finite abelian group of rank m, M an oriented compact connected surface, and F(G, M) the set of all orientation preserving free G-actions on M. Two actions φ1, φ2εF(G, M) are equivalent if there exists an orientation preserving homeomorphism h of M such that
hφ1(f) for all f ε G.