Reflections on discriminating groups

Abstract

Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [7]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R′ is non-discriminating. © Walter de Gruyter 2007.