15.86 (2002)

A group $G$ is called discriminating if for any finite set of nontrivial elements of the direct square $G \times G$ there is a homomorphism $G \times G \to G$ which does not annihilate any of them (G. Baumslag, A. G. Myasnikov, V. N. Remeslennikov). A group $G$ is called squarelike if $G$ is universally equivalent (in the sense of first order logic) to a discriminating group (B. Fine, A. M. Gaglione, A. G. Myasnikov, D. Spellman). Must every squarelike group be elementarily equivalent to a discriminating group?