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Finite abelian surface coverings†

Published online by Cambridge University Press:  18 May 2009

S. A. Jassim
S. A. Jassim
Affiliation:
11A Clarendon Road, Sketty, Swansea SA2 0SR, Wales
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Let G be a finite abelian group, and Y be a closed surface. The problems of classifying and enumerating the free and effective G-actions on Y modulo selfhomeomorphisms of Y and X = Y/G can be transferred into ones of classifying regular G-coverings on X. P. A. Smith [7], proved that for any prime number p there are pr(r–1)/2 equivalence classes of free (ℤp)r actions on Y provided that rℤgenus of X. This paper is devoted to the classification and the enumeration of regular G-covering surfaces, when G is any finite abelian group. Recently, A. Edmonds [2] classified the G-actions on closed surfaces by their G-bordism classes in the set (G) of free oriented G-cobordism classes of free oriented G-surfaces.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 207 - 218
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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