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Abstract
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We obtain a complete description of the integer group determinants for
,
the central product of the dihedral group of order 8 and cyclic group of
order 4.
These values are the same as the integer group determinants for
, the
direct product of the dihedral group of order 8 and cyclic group of order 2. It was
not previously known that the integer group determinants do not determine the
group.
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Keywords
integer group determinants, small groups, dihedral group,
quaternion group, central product
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Mathematical Subject Classification
Primary: 11C20, 15B36
Secondary: 11C08, 43A40
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Milestones
Received: 9 April 2023
Revised: 26 January 2024
Accepted: 13 February 2024
Published: 13 March 2024
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