Abstract
Let G be a permutation group on a finite set Ω. A subset of Ω 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) c log |G|/ logn for any primitive permutation group G of degree n. Several 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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