References & Citations
Mathematics > Group Theory
Title: A Class of Rearrangement Groups that are not Invariably Generated
(Submitted on 9 Jul 2022 (v1), last revised 26 Apr 2024 (this version, v3))
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.
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)
Link back to: arXiv, form interface, contact.