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16.35 (2006)

Solved

Is every finitely presented soluble group nilpotent-by-nilpotent-by-finite?

Contributor: J. R. J. Groves

Progress

No: for a prime $p$ the group $G = \langle a, b, c, d \mid b^a = b^p, c^a = c^p, d^a = d, c^b = c, d^c = dd^b, [d, d^b] = 1, d^p = 1 \rangle$ is soluble of derived length 3, but is not metanilpotent-by-finite. (V. V. Bludov, Letter of 27 April 2007.)

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