On finitely generated Engel branch groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-24 DOI:10.1112/jlms.12980

J. Moritz Petschick

引用次数: 0

Abstract

We construct finitely generated Engel branch groups, answering a question of Fernández-Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples of finitely generated non-nilpotent Engel groups following a construction by Golod from 1969. To do so, we exhibit groups acting on rooted trees with growing valency on which word lengths of elements are contracting very quickly under section maps. Our methods apply in principle to a wider class of iterated identities, of which the Engel words are a special case.

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关于有限生成的恩格尔分支群

我们构建了有限生成的恩格尔分支群，回答了费尔南德斯-阿尔克伯、诺斯和特雷西关于此类对象存在性的问题。特别是，我们构建的群不是零能群，这是继戈罗德（Golod）1969 年构建的群之后，第二类已知的有限生成非零能恩格尔群。为此，我们展示了作用于有根树的群，这些树的价不断增长，元素的字长在节映射下迅速收缩。我们的方法原则上适用于更广泛的迭代同素异形，恩格尔词是其中的一个特例。

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.