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In this paper, we give a refinement of a generalized Dedekind's theorem. Inaddition, we show that all possible values of integer group determinants of anygroup are also possible values of integer group determinants of its any abeliansubgroup. By applying the refinement of a generalized Dedekind's theorem, wedetermine all possible values of integer group determinants of the directproduct group of the cyclic group of order $8$ and the cyclic group of order$2$.

Generalized Dedekind's theorem and its application to integer group determinants