Geodesic
The symmetric genus spectrum of abelian groups
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 627-636.

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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.
DOI : 10.26493/1855-3974.1921.d6f
Keywords: Symmetric genus, strong symmetric genus, Riemann surface, abelian groups, genus spectrum, density 
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Coy L. May; Jay Zimmerman. The symmetric genus spectrum of abelian groups. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 627-636. doi : 10.26493/1855-3974.1921.d6f. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1921.d6f/

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