On Pyber's base size conjecture

2013/09/22 by Timothy C. Burness, Ákos Seress, Burness, Timothy +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1309.5584

openalex publication_date 2013/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a permutation group on a finite set Ω. A subset B ⊆ Ω is a base for G if the pointwise stabilizer of B in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A well known conjecture of Pyber from the early 1990s asserts that there exists an absolute constant c such that b(G) ≤ clog |G| / log n for any primitive permutation group G of degree n. Some special cases have been verified in recent years, including the almost simple and diagonal cases. In this paper, we prove Pyber's conjecture for all non-affine primitive groups.

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