V. V. Nesterov, A. V. Stepanov, “The identity with constants in a Chevalley group of type <nobr>$\mathrm F_4$</nobr>”, Algebra i Analiz, 2009, Volume 21, Issue 5,Pages <nobr>196

This article is cited in 7 papers

Research Papers

The identity with constants in a Chevalley group of type $\mathrm F_4$

V. V. Nesterov^a, A. V. Stepanov^b

^a Baltic State Technical University, St. Petersburg, Russia
^b St. Petersburg State Electrotechnical University, St. Petersburg, Russia

Abstract: 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.

MSC: 20G07

Received: 08.09.2008