Regular orbits of symmetric and alternating groups

@article{Fawcett2016RegularOO,
  title={Regular orbits of symmetric and alternating groups},
  author={Joanna B. Fawcett and E. O'Brien and J. Saxl},
  journal={Journal of Algebra},
  year={2016},
  volume={458},
  pages={21-52}
}
Given a nite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V ? This problem is equivalent to determining which primitive permutation groups of ane type have a base of size 2. In this paper, we classify the pairs (G;V ) for which G has a regular orbit on V where G is a covering group of a symmetric or alternating group and V is a faithful irreducible FG-module such that the order of F is prime and divides the order of G. 

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