Alternating subgroups of exceptional groups of Lie type

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In this paper, we examine embeddings of alternating and symmetric groups into almost simple groups of exceptional type. In particular, we prove that if the alternating or symmetric group has degree equal to 5, or 8 or more, then it cannot appear as the maximal subgroup of any almost simple exceptional group of Lie type. Furthermore, in the remaining open cases of degrees 6 and 7 we give considerable information about the possible embeddings. Note that no maximal alternating or symmetric subgroups are known in the remaining cases.

This is the first in a sequence of papers aiming to substantially improve the state of knowledge about the maximal subgroups of exceptional groups of Lie type.
Original languageEnglish
Pages (from-to)449-501
Number of pages53
JournalLondon Mathematical Society. Proceedings
Issue number3
Early online date5 May 2017
Publication statusPublished - Sept 2017


  • 20D06
  • 20G41
  • 20E28 (primary)


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