A proof of Pyber's base size conjecture

DOI10.1016/j.aim.2018.04.009zbMath1428.20005arXiv1611.09487OpenAlexW2558482094WikidataQ123005683 ScholiaQ123005683MaRDI QIDQ1647396

Zoltán Halasi, Hülya Duyan, Attila Maróti

Publication date: 26 June 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09487

zbMATH Keywords

permutation grouplinear groupdistinguishing numberminimal base size

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Primitive groups (20B15) Computational methods for problems pertaining to group theory (20-08)

Related Items

Asymmetric coloring of locally finite graphs and profinite permutation groups: Tucker's conjecture confirmed ⋮ Permutation groups with restricted stabilizers ⋮ Bases of twisted wreath products ⋮ On the Burness-Giudici conjecture ⋮ The maximal size of a minimal generating set ⋮ Minimal degree, base size, order: selected topics on primitive permutation groups ⋮ Derangements in wreath products of permutation groups ⋮ Orbit closed permutation groups, relation groups, and simple groups ⋮ Normalisers of primitive permutation groups in quasipolynomial time ⋮ Base sizes of primitive groups of diagonal type ⋮ Base sizes for primitive groups with soluble stabilisers ⋮ Bases for quasisimple linear groups ⋮ Base sizes of primitive groups: bounds with explicit constants ⋮ The distinguishing number of quasiprimitive and semiprimitive groups ⋮ On base sizes for primitive groups of product type ⋮ On the Saxl graphs of primitive groups with soluble stabilisers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples
• The base size of a primitive diagonal group.
• Normalizers of primitive permutation groups
• Base sizes for sporadic simple groups.
• Random generation of finite and profinite groups and group enumeration.
• On minimal degrees and base sizes of primitive permutation groups
• On the order of doubly transitive permutation groups
• On the order of uniprimitive permutation groups
• On the orders of primitive groups with restricted nonabelian composition factors
• On the base size and rank of a primitive permutation group
• Bases for primitive permutation groups and a conjecture of Babai
• Orbits of permutation groups on the power set
• Base sizes of primitive groups: bounds with explicit constants
• On the orders of doubly transitive permutation groups, elementary estimates
• Bases of primitive linear groups.
• Symmetry breaking in graphs
• Bases of primitive linear groups. II.
• Arithmetic results on orbits of linear groups
• Every coprime linear group admits a base of size two
• The minimal base size for a 𝑝-solvable linear group
• Base size, metric dimension and other invariants of groups and graphs
• On base sizes for symmetric groups
• Base sizes for simple groups and a conjecture of Cameron
• Minimum bases for permutation groups: The greedy approximation
• Simple groups, permutation groups, and probability
• Base Sizes and Regular Orbits for Coprime Affine Permutation Groups
• Random Permutations: Some Group-Theoretic Aspects
• Primitive Groups with no Regular Orbits on the Set of Subsets
• Character degrees and random walks in finite groups of Lie type
• Finite permutation groups with a transitive minimal normal subgroup
• The Minimal Base Size of Primitive Solvable Permutation Groups
• On Pyber’s base size conjecture
• On base sizes for actions of finite classical groups