Introducing $n$-Magic Groups and Characterizing $3$-Magic Finitely Generated Abelian Groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915760828317696 |
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| author | Bowerman, Danielle Fleece, Nicholas Insall, Matt |
| author_facet | Bowerman, Danielle Fleece, Nicholas Insall, Matt |
| contents | In this paper, we define an $n$-magic square in a group to be an $(n\times n)$ 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 $n>3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01858 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Introducing $n$-Magic Groups and Characterizing $3$-Magic Finitely Generated Abelian Groups Bowerman, Danielle Fleece, Nicholas Insall, Matt Group Theory 20K01 (Primary) 00A08, 91A46 (Secondary) In this paper, we define an $n$-magic square in a group to be an $(n\times n)$ 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 $n>3$. |
| title | Introducing $n$-Magic Groups and Characterizing $3$-Magic Finitely Generated Abelian Groups |
| topic | Group Theory 20K01 (Primary) 00A08, 91A46 (Secondary) |
| url | https://arxiv.org/abs/2308.01858 |