Binary permutation groups: alternating and classical groups

Nick Gill, Pablo Spiga

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We introduce a new approach to the study of finite binary permutation groups and, as an application of our method, we prove Cherlin’s binary groups conjecture for groups with socle a finite alternating group, and for the C1-primitive actions of the finite classical groups. Our new approach involves the notion, defined with respect to a group action, of a “beautiful subset”. We demonstrate how the presence of such subsets can be used to show that a given action is not binary. In particular, the study of such sets will lead to a resolution of many of the remaining open cases of Cherlin’s binary groups conjecture.
Original languageEnglish
Pages (from-to)1-43
Number of pages43
JournalAmerican Journal of Mathematics
Issue number1
Publication statusPublished - 1 Feb 2020


  • math.GR
  • 20B15, 20D06, 03C13


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