On Thompson Groups for Ważewski Dendrites
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908409405636608 |
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| author | Tarocchi, Matteo |
| author_facet | Tarocchi, Matteo |
| contents | We study a family of Thompson-like groups built as rearrangement groups of fractals from [BF19], each acting on a Ważewski dendrite. Each of these is a finitely generated group that is dense in the full group of homeomorphisms of the dendrite (studied in [DM19]) and has infinite-index finitely generated simple commutator subgroup, with a single possible exception. More properties are discussed, including finite subgroups, the conjugacy problem, invariable generation and existence of free subgroups. We discuss many possible generalizations, among which we find the Airplane rearrangement group $T_A$. Despite close connections with Thompson's group $F$, dendrite rearrangement groups seem to share many features with Thompson's group $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14660 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Thompson Groups for Ważewski Dendrites Tarocchi, Matteo Group Theory 20F65 (Primary) 20F38, 28A80, 20E32, 20F05, 54H11, 20F10, 20E45 (Secondary) We study a family of Thompson-like groups built as rearrangement groups of fractals from [BF19], each acting on a Ważewski dendrite. Each of these is a finitely generated group that is dense in the full group of homeomorphisms of the dendrite (studied in [DM19]) and has infinite-index finitely generated simple commutator subgroup, with a single possible exception. More properties are discussed, including finite subgroups, the conjugacy problem, invariable generation and existence of free subgroups. We discuss many possible generalizations, among which we find the Airplane rearrangement group $T_A$. Despite close connections with Thompson's group $F$, dendrite rearrangement groups seem to share many features with Thompson's group $V$. |
| title | On Thompson Groups for Ważewski Dendrites |
| topic | Group Theory 20F65 (Primary) 20F38, 28A80, 20E32, 20F05, 54H11, 20F10, 20E45 (Secondary) |
| url | https://arxiv.org/abs/2310.14660 |