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19.34 (2018)

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Let $G$ be a finitely generated group such that for every element $g \in G$ the set of commutators $\{[x, g] \mid x \in G\}$ is a subgroup of $G$. Is it true that $G$ is residually nilpotent?

Contributor: D. Gonçalves, T. Nasybullov

Progress

The answer is affirmative if $G$ is finite.

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