In this paper we continue the study of automorphism groups of constant-length substitution shifts and also their topological factors. We show that, up to conjugacy, all roots of the identity map are letter-exchanging maps, and all other non-trivial automorphisms arise from twisted compressions of another constant-length substitution. We characterize the group of roots of the identity in both the measurable and topological setting. Finally, we show that any topological factor of a constant-length substitution shift is topologically conjugate to a constant-length substitution shift via a letter-to-letter code.

中文翻译：

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自动换档的自同构

在本文中，我们继续研究恒长替换位移的自同构群及其拓扑因子。我们证明，直到共轭，恒等映射的所有根都是字母交换映射，所有其他非平凡的自同构都来自扭曲的另一个恒定长度替换的压缩。我们在可测量和拓扑设置中描述了恒等根组。最后，我们表明，恒定长度替换移位的任何拓扑因子都通过字母到字母的代码在拓扑上共轭到恒定长度替换移位。