  A group $G$ is invariably generated if there exists a subset $S \subseteq G$
such that, for every choice $g_s \in G$ for $s \in S$, the group $G$ is
generated by $\{ s^{g_s} \mid s \in S \}$. In [GGJ16] Gelander, Golan and
Juschenko showed that Thompson groups $T$ and $V$ are not invariably generated.
Here we generalize this result to the larger setting of rearrangement groups,
proving that any subgroup of a rearrangement group that has a certain
transitive property is not invariably generated.
