On the subgroup separability of generalized free products of nilpotent groups

Abstract

Abstract.We prove that generalized free products of finitely generated nilpotent groups with cyclic amalgamation are subgroup separable

A free product of finitely generated nilpotent groups amalgamating a cycle that is not subgroup separable

“…Consequently one might well expect a similar result for generalized free products of nilpotent groups. The paper [13] attempts to prove this result in the same fashion as [3] by establishing two propositions and then appealing to Lemma 1 of [3]. Unfortunately Proposition 3.5 of [13], whilst true, seems to be insufficient.…”

“…The paper [13] attempts to prove this result in the same fashion as [3] by establishing two propositions and then appealing to Lemma 1 of [3]. Unfortunately Proposition 3.5 of [13], whilst true, seems to be insufficient.Counterexamples of the type claimed can readily be obtained by selecting suitable subgroups of the generalized free products constructed in [5]. Consider, for instance, G = A * a B where B = a, c : [a, c] = 1 and…”

Subgroup separability of graphs of nilpotent groups

“…The first attempt to characterize subgroup separability of free products of nilpotent groups with cyclic amalgamation was made by Tang in [13]. Nevertheless, Allenby and Doniz [2] showed that Tang's result was incorrect, by constructing a counter-example.…”