Compact groups with countable Engel sinks

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-08-30 DOI:10.1142/s1664360720500150

Evgeny Khukhro, P. Shumyatsky

引用次数: 11

Abstract

An Engel sink of an element [Formula: see text] of a group [Formula: see text] is a set [Formula: see text] such that for every [Formula: see text] all sufficiently long commutators [Formula: see text] belong to [Formula: see text]. (Thus, [Formula: see text] is an Engel element precisely when we can choose [Formula: see text].) It is proved that if every element of a compact (Hausdorff) group [Formula: see text] has a countable (or finite) Engel sink, then [Formula: see text] has a finite normal subgroup [Formula: see text] such that [Formula: see text] is locally nilpotent. This settles a question suggested by J. S. Wilson.

查看原文本刊更多论文

具有可数恩格尔汇的紧群

一个群[公式:见文]的元素[公式:见文]的恩格尔汇是一个集合[公式:见文]，使得对于每一个[公式:见文]，所有足够长的换向子[公式:见文]都属于[公式:见文]。(因此，当我们可以选择[Formula: see text]时，[Formula: see text]就是一个恩格尔元素。)证明了如果紧(Hausdorff)群[公式:见文]中的每一个元素都有一个可数的(或有限的)Engel sink，则[公式:见文]有一个有限的正规子群[公式:见文]使得[公式:见文]局部幂零。这就解决了威尔逊提出的一个问题。

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.