Regular orbits of sporadic simple groups

@article{Fawcett2018RegularOO,
  title={Regular orbits of sporadic simple groups},
  author={Joanna B. Fawcett and Jurgen Muller and E. O'Brien and Robert A. Wilson},
  journal={Journal of Algebra},
  year={2018},
  volume={522},
  pages={61-79}
}
Abstract Given a finite 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 affine type have a base of size 2. Let G be a covering group of an almost simple group whose socle T is sporadic, and let V be a faithful irreducible FG-module where F has prime order dividing | G | . We classify the pairs ( G , V ) for which G has no regular orbit on V, and determine the… Expand
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