论文标题
栅极格子和稳定的自动形态组
Gate lattices and the stabilized automorphism group
论文作者
论文摘要
我们研究了一个有限类型的稳定自动形态小组，其中具有某些粘合物，称为最终填充物业，这是在剩余的$ g $上。我们表明，稳定的自动形态基团只是单片的，即它具有独特的最小非平凡的正常亚组-Ololith-巨石 - 这也很简单。为了描述整体，我们介绍了门晶格，该晶格适用于$ g $的有限索引子组上（可逆的逻辑）门。然后，整体是由门晶格生成的组的换向器子组。如果子移位和组$ g $具有一些其他属性，则门晶格会产生一个完美的组，因此它们生成了整体。特别是，当代理小组是整数时，总是如此。在这种情况下，我们还可以表明，Gate Lattices生成了稳定的自动形态组的惰性部分。因此，我们获得了有限类型的一维混合子迁移的稳定惰性自动形态组很简单。
We study the stabilized automorphism group of a subshift of finite type with a certain gluing property called the eventual filling property, on a residually finite group $G$. We show that the stabilized automorphism group is simply monolithic, i.e. it has a unique minimal non-trivial normal subgroup -- the monolith -- which is additionally simple. To describe the monolith, we introduce gate lattices, which apply (reversible logical) gates on finite-index subgroups of $G$. The monolith is then precisely the commutator subgroup of the group generated by gate lattices. If the subshift and the group $G$ have some additional properties, then the gate lattices generate a perfect group, thus they generate the monolith. In particular, this is always the case when the acting group is the integers. In this case we can also show that gate lattices generate the inert part of the stabilized automorphism group. Thus we obtain that the stabilized inert automorphism group of a one-dimensional mixing subshift of finite type is simple.
