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arXiv · 2201.07081

On the Maximal Subgroups of $E_7(q)$ and Related Almost Simple Groups

David A. Craven
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Abstract

This paper almost classifies the maximal subgroups of $E_7(q)$ for general $q$ a power of a prime $p$. Only four potential maximal subgroups are missing: $PSL_2(7)$ (unknown for $p\neq 2,3,7$), $PSL_2(8)$ ($p=2$) and $PSL_2(9)=A_6$ ($p\neq 2,3$). In addition, there is one issue with the precise structure with the positive-dimensional maximal subgroup of type $A_2$. We are able to give a complete determination of the maximal subgroups for $E_7(q)$ for $q$ an arbitrary power of $3$ and $q=4$.

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David A. Craven. 2022-01-18. On the Maximal Subgroups of $E_7(q)$ and Related Almost Simple Groups. https://arxiv.org/abs/2201.07081

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