Universal Spectra in $$G\times {\mathbb {Z}}_p$$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-21 DOI:10.1007/s00041-024-10074-2

Weiqi Zhou

引用次数: 0

Abstract

Let G be an additive and finite Abelian group, and p a prime number that does not divide the order of G. We show that if G has the universal spectrum property, then so does $G\times {\mathbb {Z}}_p$. This is similar to and extends a previous result for cyclic groups using the same dilation trick but on non-cyclic groups as well. Inductively applying this statement on the known list of permissible G one can replace p with any square-free number that does not divide the order of G, and produce new tiling to spectral results in finite Abelian groups generated by at most two elements.

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$$G\times {\mathbb {Z}}_p$$ 中的通用光谱

让 G 是一个可加的有限阿贝尔群，p 是一个不除 G 的阶的素数。我们证明，如果 G 具有普谱性质，那么 $G\times {mathbb {Z}}_p$ 也具有普谱性质。这与之前用同样的扩张技巧对循环群得出的结果相似，但也是对非循环群得出的结果的扩展。在已知的允许 G 的列表上归纳应用这一声明，我们可以用任何不除以 G 的阶的无平方数来替换 p，从而在最多由两个元素生成的有限阿贝尔群中产生新的平铺到谱结果。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.