Generalized Dedekind's theorem and its application to integer group determinants
Naoya Yamaguchi, Yuka Yamaguchi · Journal of the Mathematical Society of Japan · 2023
In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order 8 and the cyclic group of order 2.