Obstructions for subgroups of Thompson's group $V

Proceedings for the Durham Symposium on Geometric and Cohomological Group Theory, London Mathematical Society Lecture Notes #444 (2017) Thompson's group $V$ has a rich variety of subgroups, containing all finite groups, all finitely generated free groups and all finitely generated abelian groups, the finitary permutation group of a countable set, as well as many wreath products and other families of groups. Here, we describe some obstructions for a given group to be a subgroup of $V$.