2023/08/03 by D. A. Bowerman, Bowerman, Danielle, Nicholas Fleece +3
Computer Science · #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2308.01858
In this paper, we define an n-magic square in a group to be an (n× n) array of group elements whose rows, columns, and diagonals have the same product. This definition is akin to the idea of magic squares in the integers. Groups that have an n-magic square are said to be n-magic. We begin with some preliminary results and focus much of our attention on 3-magic groups. Through a series of propositions, we ultimately prove a characterization theorem for 3-magic finitely generated abelian groups. We then discuss some additional results about non-abelian groups as well as n-magic groups where n>3.