论文标题
$ \ mathrm {out}的多项式增长和子组（f _ {\ tt n}）$
Polynomial growth and subgroups of $\mathrm{Out}(F_{\tt n})$
论文作者
论文摘要
本文是一系列三篇论文中的最后一篇，研究了$ \ mathrm {out}元素的动态属性（f _ {\ tt n}）$，即非阿比亚自由组$ f _ {\ tt n} $的外部自动形态组。我们证明，对于每个子组$ h $的$ \ mathrm {out}（f _ {\ tt n}）$，存在一个元素$ n $ in h $，以至于对于每个元素$ g $ g $ g $ f _ {\ tt n} $ $ h $的每个元素的迭代下的增长。
This paper, which is the last of a series of three papers, studies dynamical properties of elements of $\mathrm{Out}(F_{\tt n})$, the outer automorphism group of a nonabelian free group $F_{\tt n}$. We prove that, for every subgroup $H$ of $\mathrm{Out}(F_{\tt n})$, there exists an element $ϕ\in H$ such that, for every element $g$ of $F_{\tt n}$, the conjugacy class $[g]$ has polynomial growth under iteration of $ϕ$ if and only if $[g]$ has polynomial growth under iteration of every element of $H$.
