Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in . 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.
Journal of Group Theory
Baumslag, Gilbert; Fine, Benjamin; Gaglione, Anthony M.; and Spellman, Dennis, "Reflections on Discriminating Groups" (2007). Math & Computer Science Faculty Publications. 5.
G. Baumslag, B. Fine, A. M. Gaglione, and D. Spellman. Reflections on Discriminating Groups, Journal of Group Theory. 10(1), 87-99.