Irredundant bases for soluble groups
Let Δ$\Delta$ be a finite set and G$G$ be a subgroup of Sym(Δ)$\operatorname{Sym}(\Delta)$. An irredundant base for G$G$ is a sequence of points of Δ$\Delta$ yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that G$G$ is primitive and soluble....
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| Published in | The Bulletin of the London Mathematical Society Vol. 57; no. 10; pp. 3013 - 3023 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
01.10.2025
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| Online Access | Get full text |
| ISSN | 0024-6093 1469-2120 1469-2120 |
| DOI | 10.1112/blms.70137 |
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| Abstract | Let Δ$\Delta$ be a finite set and G$G$ be a subgroup of Sym(Δ)$\operatorname{Sym}(\Delta)$. An irredundant base for G$G$ is a sequence of points of Δ$\Delta$ yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that G$G$ is primitive and soluble. We determine asymptotically tight bounds for the maximum length of an irredundant base for G$G$. 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|$|G|$ odd. |
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| AbstractList | Let Δ$\Delta$ be a finite set and G$G$ be a subgroup of Sym(Δ)$\operatorname{Sym}(\Delta)$. An irredundant base for G$G$ is a sequence of points of Δ$\Delta$ yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that G$G$ is primitive and soluble. We determine asymptotically tight bounds for the maximum length of an irredundant base for G$G$. 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|$|G|$ odd. |
| Author | Roney‐Dougal, Colva M. Brenner, Sofia del Valle, Coen |
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| Copyright | 2025 The Author(s). is copyright © London Mathematical Society. |
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| References | 2001; 243 1982; 34 2021; 15 2023; 322 2005; 8 2023; 121 1982; 77 1999; 45 1992; 13 2025 2024; 56 2022; 318 1983; 35 2024; 2346 1996; 53 2022; 246 1992; 1519 |
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| Snippet | Let Δ$\Delta$ be a finite set and G$G$ be a subgroup of Sym(Δ)$\operatorname{Sym}(\Delta)$. An irredundant base for G$G$ is a sequence of points of Δ$\Delta$... |
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| Title | Irredundant bases for soluble groups |
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