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<p>We obtain a complete description of the integer group determinants for the five groups of order 18. For the cyclic group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {Z}}_{18},\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <mn>18</mn> </msub> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> these are the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(18\times 18\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>18</mn> <mo>×</mo> <mn>18</mn> </mrow> </math></EquationSource> </InlineEquation> circulant determinants with integer entries. This completes the resolution of the Taussky-Todd integer group determinant problem for all groups of order less than 20.</p>

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The integer group determinants for the groups of order 18

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Bishnu Paudel,
  • Chris Pinner

摘要

We obtain a complete description of the integer group determinants for the five groups of order 18. For the cyclic group \({\mathbb {Z}}_{18},\) Z 18 , these are the \(18\times 18\) 18 × 18 circulant determinants with integer entries. This completes the resolution of the Taussky-Todd integer group determinant problem for all groups of order less than 20.