A Class of Rearrangement Groups that are not Invariably Generated
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911854805123072 |
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| author | Perego, Davide Tarocchi, Matteo |
| author_facet | Perego, Davide Tarocchi, Matteo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04235 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Class of Rearrangement Groups that are not Invariably Generated Perego, Davide Tarocchi, Matteo Group Theory 20F65 (Primary) 20F38, 28A80, 20F05, 20E45 (Secondary) 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. |
| title | A Class of Rearrangement Groups that are not Invariably Generated |
| topic | Group Theory 20F65 (Primary) 20F38, 28A80, 20F05, 20E45 (Secondary) |
| url | https://arxiv.org/abs/2207.04235 |