We construct prime amphicheiral knots that have free period 2. This settles an open question raised by the second-named author, who proved that amphicheiral hyperbolic knots cannot admit free periods and that prime amphicheiral knots cannot admit free periods of order > 2.

中文翻译：

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具有自由周期 2 的素双手结

我们构造了自由周期为 2 的素数双手结。这解决了第二位作者提出的一个悬而未决的问题，他证明了双手双曲结不能允许自由周期，并且素双手结不能允许 > 2 的自由周期。