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11.32 (1990)

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(N. Aronszajn). Let $G$ be a connected topological group locally satisfying some identical relation $f|_U = 1$, where $U$ is a neighborhood of the identity element of $G$. Is it then true that $f|_G = 1$?

Contributor: V. P. Platonov

Progress

Editors’ comment: No, not necessarily: for any odd integer $n \geqslant 10^{10}$ there is a connected topological group such that the identity $x^n = 1$ holds in some neighborhood of unity, but not in the entire group (E. Reznichenko, I. Zyabrev, Preprint, 2024, https://arxiv.org/abs/2406.05203).

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