3 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 $\mathfrak{F}$ 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 $\mathfrak{F}$ 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…