The strong symmetric genus spectrum of abelian groups

Abstract

Let $${\mathcal {S}}$$ denote the set of positive integers that may appear as the strong symmetric genus of a finite abelian group. We obtain a set of (simple) necessary and sufficient conditions for an integer g to belong to $${\mathcal {S}}$$ . We also prove that the set $${\mathcal {S}}$$ has an asymptotic density and approximate its value.