Most primitive groups are full automorphism groups of edge-transitive hypergraphs.

DOI10.1016/j.jalgebra.2014.09.002zbMath1321.20001arXiv1404.6739OpenAlexW2129746963MaRDI QIDQ468722

László Babai, Peter J. Cameron

Publication date: 7 November 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.6739

zbMATH Keywords

primitive permutation groupsautomorphism groupsedge-transitive hypergraphs

Mathematics Subject Classification ID

Hypergraphs (05C65) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Primitive groups (20B15) Probabilistic methods in group theory (20P05)

Related Items

Finite primitive groups and edge-transitive hypergraphs ⋮ Asymptotic results for primitive permutation groups ⋮ Graphical representations of cyclic permutation groups

Cites Work

• Unnamed Item
• Unnamed Item
• On minimal degrees and base sizes of primitive permutation groups
• On groups with no regular orbits on the set of subsets
• On the order of doubly transitive permutation groups
• On the order of uniprimitive permutation groups
• On the orders of doubly transitive permutation groups, elementary estimates
• Chains of subgroups in symmetric groups
• On the orders of primitive groups
• Maximal subgroups of symmetric groups
• On a conjecture of G. E. Wall.
• Transitivity of finite permutation groups on unordered sets
• Faster Canonical Forms for Primitive Coherent Configurations
• On the length of subgroup chains in the symmetric group
• Finite Permutation Groups and Finite Simple Groups
• The 2-Transitive Permutation Representations of the Finite Chevalley Groups
• Primitive Groups with no Regular Orbits on the Set of Subsets
• Asymmetric graphs
• The probability of generating the symmetric group