Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.09640 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911616016056320 |
|---|---|
| author | Cohen, Tal Vigdorovich, Itamar |
| author_facet | Cohen, Tal Vigdorovich, Itamar |
| contents | We show that a topologically generating set $S$ of a connected compact Lie group $G$ of size larger than a fixed polynomial in the rank of $G$ must be redundant (i.e., some proper subset of $S$ still topologically generates $G$). Similar results are obtained for amenable Lie groups and for reductive algebraic groups with the Zariski topology. The quantitative bounds produced by our method are controlled by corresponding bounds for finite simple groups of Lie type. We also treat redundancy up to Nielsen transformations, thereby partially answering a few conjectures of Gelander. We show that these conjectures are implied by the Wiegold conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Maximal Size of Irredundant Generating Sets in Lie Groups and Algebraic Groups Cohen, Tal Vigdorovich, Itamar Group Theory We show that a topologically generating set $S$ of a connected compact Lie group $G$ of size larger than a fixed polynomial in the rank of $G$ must be redundant (i.e., some proper subset of $S$ still topologically generates $G$). Similar results are obtained for amenable Lie groups and for reductive algebraic groups with the Zariski topology. The quantitative bounds produced by our method are controlled by corresponding bounds for finite simple groups of Lie type. We also treat redundancy up to Nielsen transformations, thereby partially answering a few conjectures of Gelander. We show that these conjectures are implied by the Wiegold conjecture. |
| title | On the Maximal Size of Irredundant Generating Sets in Lie Groups and Algebraic Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.09640 |