Abstract
Let V be a finite vector space and G⩽GL(V) a linear group. A base of G is a set of vectors whose pointwise stabiliser in G is trivial. We prove that if G is irreducible and primitive on V, then G has a base of size at most 18log|G|/log|V|+c, where c is an absolute constant. This verifies part of a conjecture of Pyber on base sizes of primitive permutation groups.
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