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17.76 (2010)

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Does there exist a finite group $G$, with $|G| > 2$, such that there is exactly one element in $G$ which is not a commutator?

Contributor: D. MacHale

Progress

*Yes, such group do exist, and there are infinitely many examples (S. V. Skresanov, Preprint, 2025, https://arxiv.org/abs/2509.17587); two other examples are also found in (O. Hatem, D. Siniora, Int. J. Group Theory, 15, no. 3 (2026), 161–167).

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