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- W4290803153 abstract "Let $k$ be any positive integer and $G$ a compact (Hausdorff) group. Let $mf{np}_k(G)$ denote the probability that $k+1$ randomly chosen elements $x_1,dots,x_{k+1}$ satisfy $[x_1,x_2,dots,x_{k+1}]=1$. We study the following problem: If $mf{np}_k(G)>0$ then, does there exist an open nilpotent subgroup of class at most $k$? The answer is positive for profinite groups and we give a new proof. We also prove that the connected component $G^0$ of $G$ is abelian and there exists a closed normal nilpotent subgroup $N$ of class at most $k$ such that $G^0N$ is open in $G$." @default.
- W4290803153 created "2022-08-12" @default.
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- W4290803153 date "2022-08-09" @default.
- W4290803153 modified "2023-10-16" @default.
- W4290803153 title "Nilpotent probability of compact groups" @default.
- W4290803153 doi "https://doi.org/10.48550/arxiv.2208.04666" @default.
- W4290803153 hasPublicationYear "2022" @default.
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