论文标题
广义Dedekind的定理及其在整数组决定因素上的应用
Generalized Dedekind's theorem and its application to integer group determinants
论文作者
论文摘要
在本文中，我们对Dedekind定理进行了改进。此外，我们表明，任何组的整数组决定因素的所有可能值也是其任何Abelian子组的整数组决定因素的可能值。通过应用广义Dedekind定理的完善，我们确定了订单$ 8 $的Cyclic Group的直接产品组的整数组决定因素的所有可能值和订单订单$ 2 $的循环组。
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 $2$.
