A group is invariably generated if there exists a subset such that, for every choice for , the group is generated by . Gelander, Golan, and Juschenko ( J. Algebra 478 (2016), 261–270) showed that Thompson groups and 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.
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Perego et al. (2024) studied this question.
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