On relational complexity and base size of finite primitive groups

Veronica Kelsey; Colva Mary Roney-Dougal

doi:10.2140/pjm.2022.318.89

On relational complexity and base size of finite primitive groups

Veronica Kelsey^*, Colva Mary Roney-Dougal

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we show that if G is a primitive subgroup of S_n that is not large base, then any irredundant base for G has size at most 5 log n. This is the first logarithmic bound on the size of an irredundant base for such groups, and is best possible up to a multiplicative constant. As a corollary, the relational complexity of G is at most 5 log n+1, and the maximal size of a minimal base and the height are both at most 5 log n. Furthermore, we deduce that a base for G of size at most 5 log n can be computed in polynomial time.

Original language	English
Pages (from-to)	89–108
Journal	Pacific Journal of Mathematics
Volume	318
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2022.318.89
Publication status	Published - 1 Aug 2022

Keywords

Permutation group
Base size
Relational complexity
Computational complexity

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Kelsey-2022-On-relational-complexity-PJM-v318-n1-p05-p
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title = "On relational complexity and base size of finite primitive groups",

abstract = "In this paper we show that if G is a primitive subgroup of Sn that is not large base, then any irredundant base for G has size at most 5 log n. This is the first logarithmic bound on the size of an irredundant base for such groups, and is best possible up to a multiplicative constant. As a corollary, the relational complexity of G is at most 5 log n+1, and the maximal size of a minimal base and the height are both at most 5 log n. Furthermore, we deduce that a base for G of size at most 5 log n can be computed in polynomial time.",

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AB - In this paper we show that if G is a primitive subgroup of Sn that is not large base, then any irredundant base for G has size at most 5 log n. This is the first logarithmic bound on the size of an irredundant base for such groups, and is best possible up to a multiplicative constant. As a corollary, the relational complexity of G is at most 5 log n+1, and the maximal size of a minimal base and the height are both at most 5 log n. Furthermore, we deduce that a base for G of size at most 5 log n can be computed in polynomial time.

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KW - Base size

KW - Relational complexity

KW - Computational complexity

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JF - Pacific Journal of Mathematics

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On relational complexity and base size of finite primitive groups

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Base size and generating graphs of primitive permutation groups

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On relational complexity and base size of finite primitive groups

Abstract

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Student theses

Base size and generating graphs of primitive permutation groups

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