SL(3, 3) is not a maximal subgroup of the Lie group of type F4 Original Research Article

We show that SL(3, 3) does not occur in F4(image) as a finite maximal subgroup by establishing that each subgroup isomorphic to SL(3, 3) normalizes an elementary abelian subgroup of F4(image) of order 27. We also show that SL(3, 3) acting with a fixed action on the split Jordan algebra associated with F4 for any field of characteristic not 2 or 3 preserves a unique Jordan algebra structure.