2020/01/18 by Kady Hossner Boden, Michael B. Ward, Boden, Kady Hossner +1
Engineering · #20D99 #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2001.06711
openalex publication_date 2020/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Cayley-Sudoku table of a finite group G is a Cayley table for G subdivided into uniformly sized rectangular blocks, in such a way that each group element appears once in each block. They were introduced by J. Carmichael, K. Schloeman, and M. B. Ward [CSW], who also gave three ways to construct them. This paper has four aims. First, we review Constructions 1 and 2 of [CSW] and uncover their unexpected heritage in the work of R. Baer and J. Denes. Next we turn to some new instances of Construction 2 inspired by Baer, which answer an open question in [CSW]. Third, we provide a very brief outline of recent reinventions of special cases of Construction 1 in the literature. We conclude with an invitation to seek out the heritage of Construction 3. Portions of this paper appear in: Kady Hossner Boden and Michael B. Ward (2019) A New Class of Cayley-Sudoku Tables, Mathematics Magazine, 92:4, 243-251, DOI: 10.1080/0025570X.2019.1613949