A class of rearrangement groups that are not invariably generated

A group (Formula presented.) is invariably generated if there exists a subset (Formula presented.) such that, for every choice (Formula presented.) for (Formula presented.), the group (Formula presented.) is generated by (Formula presented.). Gelander, Golan, and Juschenko (J. Algebra 478 (2016), 261–270) showed that Thompson groups (Formula presented.) and (Formula presented.) 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.