Scholarlink

Let \(\varGamma \) be a finite additive Abelian group. A subgroup magic rectangle is an \(m\times n\) array \(\mathbb {S}=(\zeta _{ij})\) , where \(\zeta _{ij} \in \varGamma \) for all i, j and \(|\varGamma |=mn\) , each element appears exactly once in such a way that the set of all row-sums forms a subgroup of order m and the set of all column-sums forms a subgroup of order n. This combinatorial object is a generalization of the constant sum partition of a finite Abelian group and group magic rectangle. In this article, we prove the existence of a subgroup magic rectangle over Abelian group \(\varGamma \) of order \(p^3\) , where p is an odd prime and a characterization for the existence of a subgroup magic rectangle over  \(\mathbb {Z}_{mn}\) , where \(\gcd (m,n)\) is odd.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Existence of a Subgroup Magic Rectangle

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • S. Karthik,
  • Aruna Venkatesan,
  • Krishnan Paramasivam

摘要

Let \(\varGamma \) be a finite additive Abelian group. A subgroup magic rectangle is an \(m\times n\) array \(\mathbb {S}=(\zeta _{ij})\) , where \(\zeta _{ij} \in \varGamma \) for all i, j and \(|\varGamma |=mn\) , each element appears exactly once in such a way that the set of all row-sums forms a subgroup of order m and the set of all column-sums forms a subgroup of order n. This combinatorial object is a generalization of the constant sum partition of a finite Abelian group and group magic rectangle. In this article, we prove the existence of a subgroup magic rectangle over Abelian group \(\varGamma \) of order \(p^3\) , where p is an odd prime and a characterization for the existence of a subgroup magic rectangle over  \(\mathbb {Z}_{mn}\) , where \(\gcd (m,n)\) is odd.