具有满足幂零定律的一组正哈尔测度的紧群

IF 0.8 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-27 DOI:10.1017/S0305004121000542

A. Abdollahi, Meisam Soleimani Malekan

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引用次数: 1

摘要

摘要Martino, Tointon, Valiunas和Ventura在[4，问题1·20]中提出了以下问题:设G是紧群，假设\[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\]在$G^{k+1}$中具有正Haar测度。G是否有开放的k阶幂零子群?我们给$k = 2$一个正的答案。

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Compact groups with a set of positive Haar measure satisfying a nilpotent law

Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.