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Mathematics > Group Theory

Title: A Class of Rearrangement Groups that are not Invariably Generated

Abstract: 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.
Comments: Small changes that reflect the published version (especially theorem numeration)
Subjects: Group Theory (math.GR)
MSC classes: 20F65 (Primary) 20F38, 28A80, 20F05, 20E45 (Secondary)
Journal reference: Bull. London Math. Soc. (2024)
DOI: 10.1112/blms.13046
Cite as: arXiv:2207.04235 [math.GR]
  (or arXiv:2207.04235v3 [math.GR] for this version)

Submission history

From: Matteo Tarocchi [view email]
[v1] Sat, 9 Jul 2022 09:37:03 GMT (596kb,D)
[v2] Wed, 21 Sep 2022 13:14:33 GMT (597kb,D)
[v3] Fri, 26 Apr 2024 14:38:58 GMT (597kb,D)

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