The Relatively Free Groups F(Nc∧A2) Satisfy Noncentral Commutative Transitivity. (1st October 2014) - Gaglione, Anthony M.; Lipschutz, Seymour; Spellman, Dennis
Abstract : We prove that a free group, F ( N c ∧ A 2 ), relative to the variety, N c ∧ A 2, of all groups simultaneously nilpotent of class at most c and metabelian is such that the centralizer of every noncentral element is abelian. We relate that result to the model theory of such groups as well as a quest to find a relative analog in N c ∧ A 2 of a classical theorem of Benjamin Baumslag. We also touch briefly on similar considerations in the varieties N c of nilpotent groups.