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Compact groups with a set of positive Haar measure satisfying a nilpotent law
Published online by Cambridge University Press: 19 July 2021
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
\[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\]
$G^{k+1}$
. Does G have an open k-step nilpotent subgroup?
We give a positive answer for
$k = 2$
.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 2 , September 2022 , pp. 329 - 332
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
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