Note on a magic rectangle set on dihedral group
Sylwia Cichacz

TL;DR
This paper studies the existence of magic rectangle sets over dihedral groups, proving they exist for all even dimensions and broadening the understanding of magic rectangles and squares in group theory.
Contribution
It establishes the existence of $ ext{MRS}_ ext{Γ}(m,n;k)$ for all dihedral groups of order $mnk$ when $m$ and $n$ are even, expanding prior results.
Findings
Magic rectangle sets exist over dihedral groups of order $mnk$ for even $m$ and $n$.
Broad existence results for magic rectangles and squares over dihedral groups.
Provides constructive proofs for the existence of these structures.
Abstract
Let be a group of order and be a collection of arrays whose entries are all distinct elements of . If there exist elements such that for every row , there exists an ordering of elements such that and for every column there exists an ordering of elements such that then is called a \emph{-magic rectangle set}. We investigate magic rectangle sets over dihedral groups and prove that exists for every dihedral group of order , provided that and are even. As a consequence, we obtain broad existence results for magic rectangles and magic…
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