Bases for primitive permutation groups and a conjecture of Babai

DOI10.1006/jabr.1997.7149zbMath0897.20005OpenAlexW1996938202WikidataQ123138859 ScholiaQ123138859MaRDI QIDQ1378433

David Gluck, Aner Shalev, Seress, Ákos

Publication date: 6 August 1998

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

Full work available at URL: https://semanticscholar.org/paper/15dbe045dc4d384d9afe827b266d5c6e9dc478e6

zbMATH Keywords

primitive permutation groupsbasesbase sizes

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Primitive groups (20B15)

Related Items (12)

A proof of Pyber's base size conjecture ⋮ Asymmetric coloring of locally finite graphs and profinite permutation groups: Tucker's conjecture confirmed ⋮ Permutation groups with restricted stabilizers ⋮ Bases of twisted wreath products ⋮ Minimal degree, base size, order: selected topics on primitive permutation groups ⋮ A Faster Isomorphism Test for Graphs of Small Degree ⋮ Base sizes of primitive groups: bounds with explicit constants ⋮ Deterministic polynomial factoring over finite fields: a uniform approach via \(\mathcal{P}\)-schemes ⋮ Generators and commutators in finite groups; abstract quotients of compact groups. ⋮ Simple groups, permutation groups, and probability ⋮ On Pyber’s base size conjecture ⋮ Bases of primitive linear groups.

Cites Work

• On groups with no regular orbits on the set of subsets
• On the orders of primitive groups with restricted nonabelian composition factors
• Isomorphism of graphs of bounded valence can be tested in polynomial time
• Chains of subgroups in symmetric groups
• Minimal Degrees of Primitive Permutation Groups, with an Application to Monodromy Groups of Covers of Riemann Surfaces
• Generators for Finite Simple Groups, with Applications to Linear Groups
• 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
• The Minimal Base Size of Primitive Solvable Permutation Groups
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