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
23 Citations
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