On Pyber's base size conjecture

Abstract

Let $G$ be a permutation group on a finite set $\Omega$. A subset $B\subseteq \Omega$ 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 $b(G)\le c\log |G|/\log n$ 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.

18 pages; to appear in Trans. Amer. Math. Soc

References in corpus (1)

• The base size of a primitive diagonal group