Free products of bi-orderable groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910377991733248 |
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| author | Muliarchyk, Kyrylo |
| author_facet | Muliarchyk, Kyrylo |
| contents | We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering. Our method relies on the dynamical realization of bi-ordered groups. We also show that the natural action of the automorphism group $Aut(F_2)$ on $F_2$ does not have dense orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free products of bi-orderable groups Muliarchyk, Kyrylo Group Theory 05F15, 20F60 We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering. Our method relies on the dynamical realization of bi-ordered groups. We also show that the natural action of the automorphism group $Aut(F_2)$ on $F_2$ does not have dense orbits. |
| title | Free products of bi-orderable groups |
| topic | Group Theory 05F15, 20F60 |
| url | https://arxiv.org/abs/2403.14779 |