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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.11982 |
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| _version_ | 1866912304262545408 |
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| author | Sheng, Xiaobing |
| author_facet | Sheng, Xiaobing |
| contents | Motivated by Burillo, Cleary and Roever's summary on obstructions of subgroups of Thompson's group $V,$ we explored the higher dimensional version of the groups, Brin-Thompson groups $nV$ and $SV,$ a class of infinite dimensional Brin-Thompson groups and an easy class of the twisted version of the Brin-Thompson groups $SV_G$ with some certain condition. We found that they have similar obstructions as Thompson's group $V$ on the torsion subgroups and a selection of the interesting Baumslag-Solitor groups are excluded as the subgroups of $SV$ and $SV_G.$ We also discuss a little on the group $\mathscr{S}V,$ an even larger class relaxing some of the "finiteness condition" and observe that some of the restrictions on subgroups disappear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11982 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some obstructions on the subgroups of the Brin-Thompson groups and a selection of twisted Brin-Thompson groups Sheng, Xiaobing Group Theory 20F56, 20F50 Motivated by Burillo, Cleary and Roever's summary on obstructions of subgroups of Thompson's group $V,$ we explored the higher dimensional version of the groups, Brin-Thompson groups $nV$ and $SV,$ a class of infinite dimensional Brin-Thompson groups and an easy class of the twisted version of the Brin-Thompson groups $SV_G$ with some certain condition. We found that they have similar obstructions as Thompson's group $V$ on the torsion subgroups and a selection of the interesting Baumslag-Solitor groups are excluded as the subgroups of $SV$ and $SV_G.$ We also discuss a little on the group $\mathscr{S}V,$ an even larger class relaxing some of the "finiteness condition" and observe that some of the restrictions on subgroups disappear. |
| title | Some obstructions on the subgroups of the Brin-Thompson groups and a selection of twisted Brin-Thompson groups |
| topic | Group Theory 20F56, 20F50 |
| url | https://arxiv.org/abs/2209.11982 |