Characterized Subgroups Related to some Non-arithmetic Sequence of Integers

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-03 DOI:10.1007/s00009-024-02708-y

Pratulananda Das, Ayan Ghosh

引用次数: 0

Abstract

A subgroup H of the circle group \({\mathbb {T}}\) is called characterized by a sequence of integers \((u_n)\) if \(H=\{x\in {\mathbb {T}}: \lim _{n\rightarrow \infty } u_nx=0\}\). In this note, we primarily consider a non-arithmetic sequence arising out of an arithmetic sequence in line of Bíró et al. (Stud Sci Math Hung 38: 97–113, 2001) and investigate the corresponding characterized subgroup thoroughly which includes its cardinality aspects. The whole investigation reiterates that these characterized subgroups are infinitely generated unbounded torsion countable subgroups of the circle group \({\mathbb {T}}\). Finally, we delve into certain structure theoretic observations.

查看原文本刊更多论文

与某些非算术整数序列相关的特征子群

如果 \(H=\{x\in {\mathbb {T}}: \lim _{n\rightarrow \infty } u_nx=0\}\), 则圆组 \({\mathbb {T}}\) 的子群 H 称为由整数序列 \((u_n)\) 表征的。在本注释中，我们将根据比罗等人的研究（Stud Sci Math Hung 38: 97-113, 2001），主要考虑由算术数列产生的非算术数列，并深入研究相应的特征子群，包括其心性方面。整个研究重申了这些特征子群是圆组 \({\mathbb {T}}\) 的无限生成无界扭转可数子群。最后，我们将深入探讨某些结构理论观察结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.