The strong symmetric genus of a group G is the minimum genus of any compact surface on which G acts faithfully while preserving orientation. We investigate the set of positive integers which occur as the strong symmetric genus of a finite abelian group. This is called the strong symmetric genus spectrum. We prove that there are an infinite number of gaps in the strong symmetric genus spectrum of finite abelian groups. We also determine an upper bound for the size of a finite abelian group that can act faithfully on a surface of a particular genus and then find the genus of abelian groups in particular families. These formulas produce a lower bound for the density of the strong symmetric genus spectrum.
Dr. Coy L. May and Dr. Jay Zimmerman, Department of Mathematics, Towson University
Borror, Breanna; Morris, Allison; and Tarr, Michelle
"The Strong Symmetric Genus Spectrum of Abelian Groups,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss2/8