有理截面、有界生成和群上的阶数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-23 DOI:10.1112/jlms.12920

Corentin Bodart

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引用次数: 0

摘要

我们利用有界生成和群上有理阶的联系，提供了无有理截面群（也称正则常形）的新例子。我们的例子包含第一个格里高丘克群的有限呈现 HNN 扩展。最后这个群是第一个具有可解字问题且无有理截面的有限呈现群的例子。它也不是自堆叠的，而且没有左规则完整重写系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Rational cross-sections, bounded generation, and orders on groups

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Rational cross-sections, bounded generation, and orders on groups

We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Our examples contain a finitely presented HNN-extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word problem and without rational cross-sections. It is also not autostackable, and has no left-regular complete rewriting system.

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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.