On Pyber's base size conjecture

Let G be a permutation group on a finite set S. A subset of S is a base for G if its pointwise stabilizer 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) is at most 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.