Alternating Subgroups of Exceptional Groups of Lie Type

Abstract

In this paper we examine embeddings of alternating groups and symmetric groups into almost simple groups of exceptional type. In particular, we prove that unless the alternating or symmetric group has degree 6 or 7, there is no maximal subgroup of any almost simple group with socle an exceptional group of Lie type that is an alternating or symmetric group. Furthermore, in the remaining open cases 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.

55 pages

References in corpus (3)

• Irreducible A_1 Subgroups of Exceptional Algebraic Groups
• On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
• The structure of projective indecomposable modules for $A_n$, $n\le 12$

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• On fixed-point-free involutions in actions of finite exceptional groups of Lie type
• Subspace stabilizers and maximal subgroups of exceptional groups of Lie type
• Maximal $\mathrm{PS}{\mathrm{L}}_2$ subgroups of exceptional groups of Lie type