English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This article produces a complete list of all maximal subgroups of the finitesimple groups of type $F_4$, $E_6$ and twisted $E_6$ over all finite fields.Along the way, we determine the collection of Lie primitive almost simplesubgroups of the corresponding algebraic groups. We give the stabilizers underthe actions of outer automorphisms, from which one can obtain completeinformation about the maximal subgroups of all almost simple groups with socleone of these groups. We also provide a new maximal subgroup of ${}^2\!F_4(8)$,correcting the maximal subgroups for that group from the list of Malle. Thisprovides the first new exceptional groups of Lie type to have their maximalsubgroups enumerated for three decades. The techniques are a mixture ofalgebraic groups, representation theory, computational algebra, and use of thetrilinear form on the $27$-dimensional minimal module for $E_6$. We provide acollection of auxiliary Magma files that prove the author's computationalclaims, yielding existence and the number of conjugacy classes of all maximalsubgroups mentioned in the text.

The Maximal Subgroups of the Exceptional Groups $F_4(q)$, $E_6(q)$ and ${}^2E_6(q)$ and Related Almost Simple Groups