Abstract We generalize a well-known periodicity lemma from the case of free groups to the case of acylindrically hyperbolic groups. This generalization has been used to describe solutions of certain equations in acylindrically hyperbolic groups and to characterize verbally closed finitely generated acylindrically hyperbolic subgroups of finitely presented groups.

中文翻译：

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圆柱双曲群的周期性定理

摘要 我们将一个众所周知的周期性引理从自由群的情况推广到圆柱双曲群的情况。这种推广已被用于描述圆柱双曲群中某些方程的解，并表征有限呈现群的口头封闭有限生成圆柱双曲子群。