Irredundant bases for soluble groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918068728365056 |
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| author | Brenner, Sofia del Valle, Coen Roney-Dougal, Colva M. |
| author_facet | Brenner, Sofia del Valle, Coen Roney-Dougal, Colva M. |
| contents | Let $Δ$ be a finite set and $G$ be a subgroup of $\operatorname{Sym}(Δ)$. An irredundant base for $G$ is a sequence of points of $Δ$ yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that $G$ is primitive and soluble. We determine asymptotically tight bounds for the maximum length of an irredundant base for $G$. Moreover, we disprove a conjecture of Seress on the maximum length of an irredundant base constructed by the natural greedy algorithm, and prove Cameron's Greedy Conjecture for $|G|$ odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irredundant bases for soluble groups Brenner, Sofia del Valle, Coen Roney-Dougal, Colva M. Group Theory 20B15 (Primary), 20D10, 20E15 (Secondary) Let $Δ$ be a finite set and $G$ be a subgroup of $\operatorname{Sym}(Δ)$. An irredundant base for $G$ is a sequence of points of $Δ$ yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that $G$ is primitive and soluble. We determine asymptotically tight bounds for the maximum length of an irredundant base for $G$. Moreover, we disprove a conjecture of Seress on the maximum length of an irredundant base constructed by the natural greedy algorithm, and prove Cameron's Greedy Conjecture for $|G|$ odd. |
| title | Irredundant bases for soluble groups |
| topic | Group Theory 20B15 (Primary), 20D10, 20E15 (Secondary) |
| url | https://arxiv.org/abs/2501.03003 |