论文标题
来自“相似”群体的霍顿样小组
Houghton-like groups from "shift-similar" groups
论文作者
论文摘要
我们介绍和研究\ emph {shift-similar} $ g \ le \ le \ textrm {sym}（\ mathbb {n}）$，它们在霍顿群体的世界中发挥了相似的作用，这些群体在汤普森团体中扮演了自我类似的群体。我们还介绍了霍顿式的$ h_n（g）$，该$ h_n（g）$是由换档组$ g $引起的，这是汤普森团体世界的Röver-Nekrashevych群体的类似物。我们证明了有关移动相似的组和这些类似霍顿的群体的各种结果，包括有关有限产生和敏感性的结果。一个显着的结果是，与自相似的组相比，每个有限生成的组都嵌入有限生成的移位类似群的亚组，而不是这种情况。这特别是与自我相似的情况相反，有许多有限生成的相似群体的同构类别类似的同构类别。
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.
