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arXiv · 2101.11507

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

Alireza Abdollahi·Meisam soleimani Malekan
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Abstract

The following question is proposed in [4, Question 1.20]: Let $G$ be a compact group, and suppose that $$\mathcal{N}_k(G) = \{(x1,\dots,x_{k+1}) \in G^{k+1} \;\|; [x_1,\dots, x_{k+1}] = 1\}$$ has positive Haar measure in $G^{k+1}$. Does $G$ have an open $k$-step nilpotent subgroup? The case $k = 1$ is already known. We positively answer it for $k = 2$.

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Alireza Abdollahi, Meisam soleimani Malekan. 2021-01-27. Compact groups with a set of positive Haar measure satisfying a nilpotent law. https://doi.org/10.1017/s0305004121000542

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