全移位的有限点上的传递作用与有限Ryan定理
Transitive action on finite points of a full shift and a finitary Ryan's theorem
摘要：
我们表明，在四个符号的全移位，有一个生成子群的自同构群的行动是（集理论）传递的所有订单上的有限支持点，必要的警告，由于移位换向。作为推论，我们得到，有一个有限集的自同构集的中心化是$\mathbb{Z}$（移位组），给出了有限版本的瑞安定理（四符号全移位），提出了一个自同构群不变的混合SFT。我们表明，任何这样的自同构集必须生成一个无限群，也表明，也有一个组的这种传递性的性质，这是一个子群的换位子群，其元素可以被写入的组合对合。我们提出了许多相关的问题，并证明了可逆图灵机群，拓扑完全群和Thompson的~ $V$的一些简单的传递性结果。
英文摘要：
We show that on the four-symbol full shift, there is a finitely generated subgroup of the automorphism group whose action is (set-theoretically) transitive of all orders on the points of finite support, up to the necessary caveats due to shift-commutation. As a corollary, we obtain that there is a finite set of automorphisms whose centralizer is $\mathbb{Z}$ (the shift group), giving a finitary version of Ryan's theorem (on the four-symbol full shift), suggesting an automorphism group invariant for mixing SFTs. We show that any such set of automorphisms must generate an infinite group, and also show that there is also a group with this transitivity property which is a subgroup of the commutator subgroup and whose elements can be written as compositions of involutions. We ask many related questions and prove some easy transitivity results for the group of reversible Turing machines, topological full groups and Thompson's~$V$.
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