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17.46 (2010)

Solved

Let $G$ be a finite $p$-group in which every 2-generator subgroup has cyclic derived subgroup. Is the derived length of $G$ bounded?
If $p \neq 2$, then $G^{(2)} = 1$ (J. Alperin), but for $p = 2$ there are examples with $G^{(2)}$ cyclic and elementary abelian of arbitrary order.

Contributor: B. M. Veretennikov

Progress

Yes, it is at most 4 (B. Wilkens, J. Group Theory, 17, no. 1 (2014), 151–174).

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