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Let $w$ be a group word, and $G$ a profinite group. Is it true that the cardinality of the set of $w$-values in $G$ is either finite or at least continuum?

Contributor: P. Shumyatsky

Progress

An affirmative answer is known for several important words; see (E. Detomi, B. Klopsch, P. Shumyatsky, J. London Math. Soc. (2), 102 (2020), 977–993).

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