Geodesic
The identity with constants in a Chevalley group of type $\mathrm F_4$
Algebra i analiz, Tome 21 (2009) no. 5, pp. 196-202 
V. V. Nesterov; A. V. Stepanov. The identity with constants in a Chevalley group of type $\mathrm F_4$. Algebra i analiz, Tome 21 (2009) no. 5, pp. 196-202. http://geodesic.mathdoc.fr/item/AA_2009_21_5_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

N. L. Gordeev proved that a generalized group identity holds in Chevalley groups with multiply laced root systems. It was also shown that a stronger identity is valid for the Chevalley groups of types $\mathrm{B}_l$ and $\mathrm{C}_l$. In the present paper, it is proved that this strong identity is fulfilled in Chevalley groups of type $\mathrm{F}_4$ and fails to be true in Chevalley groups of type $\mathrm{G}_2$. The main result of the paper is the last ingredient in the proof of the claim that the lattice of intermediate subgroups between $G(\mathrm{F}_4,R)$ and $G(\mathrm{F}_4,A)$ is standard for an arbitrary pair of rings $R\subseteq A$ with $2$ invertible.

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