论文标题
随机替代次要的自多态家群体
Automorphism groups of random substitution subshifts
论文作者
论文摘要
我们证明，对于合适的随机替换类别，它们相应的子缩影具有包含无限简单亚组和完整移动的自动形态组的副本的自动形态组。因此，它们是可数的，不可分割的，并且是非进攻有限的。为了证明这一点，我们介绍了随机替代的造成混乱和广泛的造成的概念，以及对将具有独立关注的随机替换的局部识别性。没有可识别性，我们需要更精致的识别词才能理解其自动形态。我们表明，单个可识别的单词的存在通常足以嵌入随机替代子移动的自动形态群体完全转移的自动形态群体。
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local version of recognisability for random substitutions that will be of independent interest. Without recognisability, we need a more refined notion of recognisable words in order to understand their automorphisms. We show that the existence of a single recognisable word is often enough to embed the automorphism group of a full shift in the automorphism group of the random substitution subshift.
