Residual Properties of Free Products of Infinitely Many Nilpotent Groups Amalgamating Cycles Original Research Article

We prove that a free product of infinitely many finitely generated, torsion free, nilpotent groups amalgamating isolated cycles is residually finite-pfor all primespso long as the number of generators and nilpotency class of the factors are both bounded. Examples illustrate that if we remove any single hypothesis, the resulting group need not even be residually finite.