论文标题
全班自动形态组中的失真元素
Distortion element in the automorphism group of a full shift
论文作者
论文摘要
我们表明，在完整移动的自动形态组的有限生成的亚组$ g $中有一个失真元素，即无限顺序的元素，其单词norm norm从polylogarithmithmithmithmithmithmity上生长。作为推论，我们在包含$ g $副本的任何子缩合的熵尺寸上获得下限，并且仅当且仅当Sofic Shift无法达到无数时。我们还获得了Turing机器和高维的Brin-Thompson组$ MV $接纳失真元素的组；特别是，$ 2V $（与$ V $不同）不承认对CAT $（0）$ Cube Complex的适当操作。失真元素本质上是智能机器。
We show that there is a distortion element in a finitely-generated subgroup $G$ of the automorphism group of the full shift, namely an element of infinite order whose word norm grows polylogarithmically. As a corollary, we obtain a lower bound on the entropy dimension of any subshift containing a copy of $G$, and that a sofic shift's automorphism group contains a distortion element if and only if the sofic shift is uncountable. We obtain also that groups of Turing machines and the higher-dimensional Brin-Thompson groups $mV$ admit distortion elements; in particular, $2V$ (unlike $V$) does not admit a proper action on a CAT$(0)$ cube complex. The distortion element is essentially the SMART machine.
