The symmetric genus spectrum of abelian groups - May, Coy L. (Ars mathematica contemporanea, 2019)
Let ?$\mathcal{S}$? denote the set of positive integers that appear as the symmetric genus of a finite abelian group and let ?$\mathcal{S}_0$? 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 ?$\mathcal{S} = \mathcal{S}_0$?. As a result, we obtain a set of necessary and sufficient conditions for an integer ?$g$? to belong to ?$\mathcal{S}$?. This also shows that ?$\mathcal{S}$? has an asymptotic density and that it is approximately 0.3284.
Keywords: abelian groups; abelove grupe; density; genus spectrum; gostota; krepki simetrični rod; Riemann surface; Riemannova ploskev; simetrični rod; spekter rodu; strong symmetric genus; symmetric genus