Invariable generation of Thompson groups

A subset $S$ of a group $G$ invariably generates $G$ if $G= langle s^{g(s)} | s in Srangle$ for every choice of $g(s) in G,s in S$. 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 invariable generated by a finite set, whereas Thompson groups $T$ and $V$ are not invariable generated.