3 problems

Let $n\geq 2$, and let $G$ be strongly shift-similar, so that $H_1(G)=G$. Assume that $G$ has stronger finiteness properties than the classical Houghton group $H_n$. Stronger-finit…

Let $n$ be a positive integer, let $G\leq \operatorname{Sym}(\mathbb{N})$ be shift-similar, and let $\operatorname{F}_{n-1}$ denote the corresponding finiteness property. Finitenes…

Let $(H_n)_{n\in\mathbb{N}}$ be the Houghton groups. For $n\geq 2$, let $\chi_1,\dots,\chi_n$ be the characters defined by the eventual translation lengths, with…