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18.73 (2014)

Partially Solved

a) Does every finitely generated solvable group of derived length $l \geqslant 2$ embed into a 2-generated solvable group of length $l + 1$?
b) Does every finitely generated solvable group of derived length $l \geqslant 2$ embed into some $k$-generated $(l + 1)$-solvable group, where $k = k(l)$?

Contributor: A. Yu. Olshanskii

Progress

a) Comment of 2021: It is proved that any countable solvable group of derived length $l$ with torsion-free abelianization embeds in a 2-generated solvable group of derived length $l + 1$ (V. A. Roman’kov, Proc. Amer. Math. Soc., 149 (2021), 4133–4143).
b) It is proved that any finitely generated solvable group of derived length $l$ can be embedded in a 4-generated solvable group of derived length $l + 1$ (V. A. Roman'kov, Proc. Amer. Math. Soc., 149 (2021), 4133–4143).

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