Title of Abstract

Biplanarity of Subgroup Lattices of Finite Abelian Groups

Session Title

Additional Projects

Faculty Sponsor (for work done with a non-Winthrop mentor)

Arran Hamm, Ph.D.

College

College of Arts and Sciences

Department

Mathematics

Abstract

The subgroup lattice of a group G is the graph whose vertices are the subgroups of G and adjacency is determined by direct set containment. Recently a complete characterization has been given for the groups whose subgroup lattice is planar. Shifting gears, we say a graph is biplanar if it is the union of two planar graphs. In this research project we found partial characterizations for finite abelian groups with biplanar subgroup lattices.

Start Date

15-4-2022 12:00 PM

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Apr 15th, 12:00 PM

Biplanarity of Subgroup Lattices of Finite Abelian Groups

The subgroup lattice of a group G is the graph whose vertices are the subgroups of G and adjacency is determined by direct set containment. Recently a complete characterization has been given for the groups whose subgroup lattice is planar. Shifting gears, we say a graph is biplanar if it is the union of two planar graphs. In this research project we found partial characterizations for finite abelian groups with biplanar subgroup lattices.