源自“移位相似”群的类 Houghton 群
Houghton-like groups from "shift-similar" groups
AI总结：
本文定义移位相似群及由其构造的类 Houghton 群 H_n(G)，证明有限生成、顺从性等结果，并表明任意有限生成群均可嵌入有限生成移位相似群。
摘要：
我们引入并研究了 shift-similar（移位相似）群 G≤Sym(N)；在 Houghton 群的世界中，它们所起的作用类似于 self-similar（自相似）群在 Thompson 群世界中所起的作用。我们还引入了由移位相似群 G 产生的类 Houghton 群 H_n(G)，它们是 Thompson 群世界中 Röver–Nekrashevych 群的类比物。我们证明了关于移位相似群和这些类 Houghton 群的一系列结果，包括有限生成性和顺从性方面的结果。一个突出的结果是，每个有限生成群都可作为子群嵌入某个有限生成移位相似群中，这与自相似群的情形形成对比，在那里情况并非如此。这尤其确立了存在不可数多个有限生成移位相似群的同构类，再次与自相似情形形成对比。
英文摘要：
We introduce and study \emph{shift-similar} groups $G\le\textrm{Sym}(\mathbb{N})$, which play an analogous role in the world of Houghton groups that self-similar groups play in the world of Thompson groups. We also introduce Houghton-like groups $H_n(G)$ arising from shift-similar groups $G$, which are an analog of Röver-Nekrashevych groups from the world of Thompson groups. We prove a variety of results about shift-similar groups and these Houghton-like groups, including results about finite generation and amenability. One prominent result is that every finitely generated group embeds as a subgroup of a finitely generated shift-similar group, in contrast to self-similar groups, where this is not the case. This establishes in particular that there exist uncountably many isomorphism classes of finitely generated shift-similar groups, again in contrast to the self-similar situation.
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