Resumen de Discriminating and Squarelike Groups II: Examples

Benjamin Fine, Anthony M. Gaglione, Dennis Spellman

• Abstract. Discriminating groups were invented by G. Baumslag, A.G.

  Myasnikov and V.N. Remeslennikov in [BMR2]. These groups arose out of consideration by the above authors of their freshly minted theory of algebraic geometry over groups. Although unforeseen at first, the notion admits beautiful and exotic examples some of which appeared earlier in diverse contexts.

  Squarelike groups were invented by the authors in [FGMS2] and may be viewed as nonstandard discriminating groups. In this paper we give examples of groups which are discriminating or squarelike as well as groups which are not. The main result is the existence of a finitely generated squarelike group which is not discriminating.