Abstract
Let be an automorphism of a group which is a free product of finitely many groups each of which is freely indecomposable and two of the factors contain proper finite index characteristic subgroups. We show that G has infinitely many -twisted conjugacy classes. As an application, we show that if G is the fundamental group of a three-manifold that is not irreducible, then G has property that is, there are infinitely many -twisted conjugacy classes in G for every automorphism of G.
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