自由-循环群是方程可约的
Free-by-cyclic groups are equationally Noetherian
AI总结：
本文证明自由-循环群是方程可约的，并展示了其指数增长速率集合的良序性，同时揭示了相关群的非初等作用和分裂性质。
摘要：
一个群G被称为方程可约的，如果G中每一个方程系统都等价于一个有限子系统。我们证明所有自由-循环群都是方程可约的。作为推论，我们得出自由-循环群的指数增长速率集合是良序的。在此过程中，我们证明具有无限阶多项式增长单体的自由-循环群允许非初等的4-acylindrical作用于树上。我们证明由Bestvina-Feighn-Handel改进的相对轨型机制造成的分裂在增长至少为二次时是2-acylindrical的。
英文摘要：
A group $G$ is said to be equationally Noetherian if every system of equations in $G$ is equivalent to a finite subsystem. We show that all free-by-cyclic groups are equationally Noetherian. As a corollary, we deduce that the set of exponential growth rates of a free-by-cyclic group is well ordered. Along the way, we prove that free-by-cyclic groups with polynomially growing monodromies of infinite order admit non-elementary 4-acylindrical actions on trees. We show that the splittings arising from the improved relative train track machinery of Bestvina-Feighn-Handel are 2-acylindrical when the growth is at least quadratic.
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