6 problems

Let $F$) be Thompson's group, and let $G$ be a subgroup of $F$. A group is elementary amenable if it belongs to the class obtained from finite and abelian groups by transfinite ext…

Let $G\leq \mathrm{PL}_+ I$ be a finitely generated subgroup. An $F$-obstruction is a pair of elements of $G$ forming an $F$-obstruction in the sense of Theorem. Embedding conjectu…

Let $\mathfrak{F}$ be the partially ordered family of groups under embeddability, with order relation $\hookrightarrow$. A partial order is a well-quasi-order if it contains no inf…

Let $I$ be the interval, let $\operatorname{PL}_+(I)$ be the group of all piecewise linear elements of $\operatorname{Homeo}_+(I)$, let $H$ be a finitely generated subgroup of…

Let $\mathfrak{F}$ be the partially ordered family of relevant subgroups under embeddability, let $\varepsilon_0$ be the ordinal used to index the chain, and extend the chain by se…

Let $F$ denote Thompson group $F$, and let a group be 2-generated if it has a generating set with two elements. The finite-index generation conjecture. Every finite-index subgroup…