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17.47 (2010)

Open

Let $G$ be a nilpotent group in which every coset $x[G, G]$ for $x \notin [G, G]$ coincides with the conjugacy class $x^G$. Is there a bound for the nilpotency class of $G$?

Contributor: S. H. Ghate, A. S. Muktibodh

Progress

If $G$ is finite, then its class is at most 3 (R. Dark, C. Scoppola, J. Algebra, 181, no. 3 (1996), 787–802).

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