广义Dedekind定理及其在整数群行列式中的应用

Pub Date : 2023-11-01 DOI:10.2969/jmsj/90539053

Naoya YAMAGUCHI, Yuka YAMAGUCHI

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引用次数: 11

摘要

本文给出了广义Dedekind定理的一个改进。此外，我们证明了任意群的整群行列式的所有可能值也是其任意阿贝尔子群的整群行列式的所有可能值。通过对广义Dedekind定理的改进，我们确定了8阶循环群与2阶循环群的直积群的整群行列式的所有可能值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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