Some elementary amenable subgroups of interval exchange transformations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912862910283776 |
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| author | Guelman, Nancy Liousse, Isabelle |
| author_facet | Guelman, Nancy Liousse, Isabelle |
| contents | In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state criteria for not virtual nilpotency or solvability, and we give conditions to ensure that they are not virtually solvable. We precise their abelianizations, we determine when they are isomorphic to certain lamplighter groups and we provide non isomorphic cases among them. As consequences, in the class of infinite finitely generated subgroups of iets up to isomorphism, we exhibit infinitely many non virtually solvable and non linear groups, and infinitely many solvable groups of arbitrary derived length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23054 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some elementary amenable subgroups of interval exchange transformations Guelman, Nancy Liousse, Isabelle Group Theory Dynamical Systems 37E05, 57S30, 37C85, 20K35, 20F50 In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state criteria for not virtual nilpotency or solvability, and we give conditions to ensure that they are not virtually solvable. We precise their abelianizations, we determine when they are isomorphic to certain lamplighter groups and we provide non isomorphic cases among them. As consequences, in the class of infinite finitely generated subgroups of iets up to isomorphism, we exhibit infinitely many non virtually solvable and non linear groups, and infinitely many solvable groups of arbitrary derived length. |
| title | Some elementary amenable subgroups of interval exchange transformations |
| topic | Group Theory Dynamical Systems 37E05, 57S30, 37C85, 20K35, 20F50 |
| url | https://arxiv.org/abs/2601.23054 |