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.

中文翻译：

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自由产物中的扭曲共轭

摘要 设一个群的自同构，该群是有限多个群的自由积，每个群是自由不可分解的，其中两个因子包含适当的有限指数特征子群。我们证明 G 有无限多的扭曲共轭类。作为一个应用，我们证明如果 G 是不可约的三流形的基本群，那么 G 的性质就是，对于 G 的每个自同构，在 G 中有无限多的扭曲共轭类。