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20.98 (2022)

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Let $G$ be a group of permutations of the set of positive integers $\mathbb{N}$ isomorphic to the additive group of rational numbers. Must there be an element $g \in G$ such that the set $\{a - a^g \mid a \in \mathbb{N}\}$ is infinite?

Contributor: N. M. Suchkov

Progress

*Yes, it must (N. M. Suchkov, A. A. Shlepkin, D. A. Taysnyov, Siberian Math. J., 65 (2024), 1390–1394).

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