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On the Maximal Subgroups of $E_7(q)$ and Related Almost Simple Groups
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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 $q=4$.
Forward citations
Cited by 4 Pith papers
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For every finite nonabelian simple group T, the order |T| is bounded above by a function of m(T), the maximum number of Aut(T)-classes of p-elements over all primes p.
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Exceptional groups and the s-arc-transitivity of vertex-primitive digraphs, II
For every almost simple group with socle E7(q) or E8(q), vertex-primitive s-arc-transitive digraphs satisfy s≤2, completing the exceptional-group case of the Giudici–Xia problem.
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Flag-transitive point-primitive quasi-symmetric $2$-designs and exceptional groups of Lie type
For quasi-symmetric 2-designs with intersection numbers 0 and y between 2 and 10, the socle of any flag-transitive point-primitive automorphism group cannot be an exceptional group of Lie type.
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