TY - JOUR
T1 - Discriminating groups
AU - Fine, Benjamin
AU - Myasnikov, Alexei G.
AU - Gaglione, Anthony M.
AU - Spellman, Dennis
PY - 2001
Y1 - 2001
N2 - 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 [2]. 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.
AB - 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 [2]. 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.
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U2 - 10.1515/jgth.2001.034
DO - 10.1515/jgth.2001.034
M3 - Article
AN - SCOPUS:0035646259
SN - 1433-5883
VL - 4
SP - 463
EP - 474
JO - Journal of Group Theory
JF - Journal of Group Theory
IS - 4
ER -