Invariable generation of Thompson groups

A subset S of a group G invariably generates G if G=〈sg(s)|s∈S〉 for every choice of g(s)∈G,s∈S. We say that a group G is invariably generated if such S exists, or equivalently, if S=G invariably generates G. In this paper, we study invariable generation of Thompson groups. We show that Thompson group F is invariably generated by a finite set, whereas Thompson groups T and V are not invariably generated.