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4.39 (1973)

Solved

A countable group $U$ is said to be SQ-universal if every countable group is isomorphic to a subgroup of a quotient group of $U$. Let $G$ be a group that has a presentation with $r \geqslant 2$ generators and at most $r - 2$ defining relations. Is $G$ SQ-universal?

Contributor: A. M. Macbeath, P. M. Neumann

Progress

Yes, it is (B. Baumslag, S. J. Pride, J. London Math. Soc., 17 (1978), 425–426).

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