Subgroups and diversity of left-orderable small cancellation groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914657020674048 |
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| author | Steenbock, Markus |
| author_facet | Steenbock, Markus |
| contents | We arrange classical small cancellation constructions to produce left-orderable groups: we show that every finitely generated group is the quotient of a left-ordered small cancellation group by a finitely generated kernel (Rips construction). We give presentations of left-ordered hyperbolic small cancellation groups that are not locally indicable, and observe that the class of left-ordered small cancellation groups that are not locally indicable is quasi-isometrically diverse. Altogether, this shows that left-orderable small cancellation groups form a rich and diverse class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Subgroups and diversity of left-orderable small cancellation groups Steenbock, Markus Group Theory We arrange classical small cancellation constructions to produce left-orderable groups: we show that every finitely generated group is the quotient of a left-ordered small cancellation group by a finitely generated kernel (Rips construction). We give presentations of left-ordered hyperbolic small cancellation groups that are not locally indicable, and observe that the class of left-ordered small cancellation groups that are not locally indicable is quasi-isometrically diverse. Altogether, this shows that left-orderable small cancellation groups form a rich and diverse class. |
| title | Subgroups and diversity of left-orderable small cancellation groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2312.12120 |