The base size of a primitive diagonal group

@article{Fawcett2013TheBS,
  title={The base size of a primitive diagonal group},
  author={Joanna B. Fawcett},
  journal={Journal of Algebra},
  year={2013},
  volume={375},
  pages={302-321}
}
Abstract A base B for a finite permutation group G acting on a set Ω is a subset of Ω with the property that only the identity of G can fix every point of B . We prove that a primitive diagonal group G has a base of size 2 unless the top group of G is the alternating or symmetric group acting naturally, in which case the minimal base size of G is determined up to two possible values. We also prove that the minimal base size of G satisfies a well-known conjecture of Pyber. Moreover, we prove… Expand
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Base sizes of primitive permutation groups
On Pyber's base size conjecture
On the Saxl graphs of primitive groups with soluble stabilisers
On base sizes for algebraic groups
Primitive permutation IBIS groups
On the Saxl graph of a permutation group
Bases of twisted wreath products
Regular orbits of sporadic simple groups
A proof of Pyber's base size conjecture
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