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A complete determination of when the elements of a fundamental group of a (countable) graph of profinite groups are conjugacy distinguished is given. By embedding an arbitrary fundamental group G into one with profinite vertex groups and making use of the above result, questions on conjugacy separability of G can be reduced to the solution of equations in the vertex groups of G.doi:10.1090/s0002-9947-1992-1102891-8 fatcat:7lcgubhwp5ezhmoswzaqlnwqcy