Existence of Magic Rectangle Sets Over Finite Abelian Groups

ABSTRACT Let , and be positive integers. Let be a finite abelian group of order . A ‐magic rectangle set is a collection of arrays of size , whose entries are elements of a group , each appearing exactly once, such that the sum of each row in every array equals a constant , and the sum of each column in every array equals a constant . This paper establishes the necessary and sufficient conditions for the existence of an , for any finite abelian group , thereby confirming a conjecture posted by Cichacz and Hinc.