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18.75 (2014)

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Does every finite solvable group $G$ have the following property: there is a number $d = d(G)$ such that $G$ is a homomorphic image of every group with $d$ generators and one relation?

This property holds for finite nilpotent groups and does not hold for every non-solvable finite group; see (S. A. Zaĭtsev, Moscow Univ. Math. Bull., 52, no. 4 (1997), 42–44).

Contributor: A. Yu. Olshanskii

Progress

Yes, it does (N. Nikolov, D. Segal, Bull. London Math. Soc., 39, no. 2 (2007), 209–213).

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