A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from . We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups.
Journal of Group Theory
Fine, Benjamin; Myasnikov, A. G.; Gaglione, Anthony M.; and Spellman, Dennis, "Discriminating Groups" (2001). Math & Computer Science Faculty Publications. 8.
B. Fine, A. G. Myasnikov, A. M. Gaglione, and D. Spellman. Discriminating Groups, Journal of Group Theory. 4(4), 463-474.