The symmetric genus spectrum of abelian groups

Coy L. May, Jay Zimmerman

Abstract


Let S denote the set of positive integers that appear as the symmetric genus of a finite abelian group and let S0 denote the set of positive integers that appear as the strong symmetric genus of a finite abelian group. The main theorem of this paper is that S = S0. As a result, we obtain a set of necessary and sufficient conditions for an integer g to belong to S. This also shows that S has an asymptotic density and that it is approximately 0.3284.


Keywords


Symmetric genus, strong symmetric genus, Riemann surface, abelian groups, genus spectrum, density

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DOI: https://doi.org/10.26493/1855-3974.1921.d6f

ISSN: 1855-3974

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