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Identity with constants in a Chevalley group of type $ {\mathrm F}_4$


Authors: V. Nesterov and A. Stepanov
Translated by: the authors
Original publication: Algebra i Analiz, tom 21 (2009), nomer 5.
Journal: St. Petersburg Math. J. 21 (2010), 819-823
MSC (2010): Primary 20G07
DOI: https://doi.org/10.1090/S1061-0022-2010-01119-1
Published electronically: July 15, 2010
MathSciNet review: 2604568
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

V. Nesterov
Affiliation: Baltic State Technical University, 1-st Krasnoarmeiskaya Street 1, St. Petersburg 190005, Russia
Email: vl.nesterov@mail.ru

A. Stepanov
Affiliation: St. Petersburg Electrotechnical University, Professor Popov Street 5, St. Petersburg 197376, Russia
Email: stepanov239@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2010-01119-1
Keywords: Group identity, Chevalley group, multiply laced root system
Received by editor(s): September 8, 2008
Published electronically: July 15, 2010
Additional Notes: The second author was supported by RFBR (grant no. 08-01-00756-a).
Article copyright: © Copyright 2010 American Mathematical Society

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