The Strong Symmetric Genus Spectrum of Abelian Groups

Authors

Breanna Borror, Towson University
Allison Morris, Towson University
Michelle Tarr, Towson University

Abstract

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.

Author Bio

Breanna Borror is a mathematics major at Towson University with a concentration in secondary education. She aspires to promote a positive outlook of mathematics to her future students.

Allison Morris is finishing a Bachelor’s Degree in applied mathematics at Towson University. She plans to graduate in May of 2015 and begin her career.

Michelle Tarr is a mathematics major at Towson University with a concentration in secondary education. She hopes to teach in a local high school after graduation.

Faculty Sponsor

Coy L. May, Jay Zimmerman

Recommended Citation

Borror, Breanna; Morris, Allison; and Tarr, Michelle (2014) "The Strong Symmetric Genus Spectrum of Abelian Groups," Rose-Hulman Undergraduate Mathematics Journal: Vol. 15: Iss. 2, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss2/8