Isolated circular orders on free products of cyclic groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917359858483200 |
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| author | Jibiki, Chihaya Maruyama, Shuhei |
| author_facet | Jibiki, Chihaya Maruyama, Shuhei |
| contents | In this paper, we construct countably many isolated circular orders on the free products $G = F_{2n} \ast \mathbb{Z}_{m_1} \ast \cdots \ast \mathbb{Z}_{m_k}$ of cyclic groups. Moreover, we prove that these isolated circular orders are not the automorphic images of the others. By using these isolated circular orders, we also construct countably many isolated left orders on a certain central $\mathbb{Z}$-extension of $G$, which are not the automorphic images of the others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isolated circular orders on free products of cyclic groups Jibiki, Chihaya Maruyama, Shuhei Group Theory Dynamical Systems 06F15 (Primary) 20F60, 37E10, 22F50 (Secondary) In this paper, we construct countably many isolated circular orders on the free products $G = F_{2n} \ast \mathbb{Z}_{m_1} \ast \cdots \ast \mathbb{Z}_{m_k}$ of cyclic groups. Moreover, we prove that these isolated circular orders are not the automorphic images of the others. By using these isolated circular orders, we also construct countably many isolated left orders on a certain central $\mathbb{Z}$-extension of $G$, which are not the automorphic images of the others. |
| title | Isolated circular orders on free products of cyclic groups |
| topic | Group Theory Dynamical Systems 06F15 (Primary) 20F60, 37E10, 22F50 (Secondary) |
| url | https://arxiv.org/abs/2410.16932 |