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Width of groups of type $ {\mathrm E}_{6}$ with respect to root elements. I


Author: I. M. Pevzner
Translated by: A. Yu. Luzgarev
Original publication: Algebra i Analiz, tom 23 (2011), nomer 5.
Journal: St. Petersburg Math. J. 23 (2012), 891-919
MSC (2010): Primary 20G15
DOI: https://doi.org/10.1090/S1061-0022-2012-01222-7
Published electronically: July 10, 2012
MathSciNet review: 2918427
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Abstract: Simply connected and adjoint groups of type $ {\mathrm E}_{6}$ over fields are considered. Let $ K$ be a field such that every polynomial of degree not exceeding six has a root. It is shown that any element of the adjoint group of type $ {\mathrm E}_{6}$ over $ K$ can be expressed as a product of at most eight root elements.


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Additional Information

I. M. Pevzner
Affiliation: Herzen State Pedagogical University, Moǐka 48, St. Petersburg 191186, Russia
Email: pevzner{\textunderscore}igor@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-2012-01222-7
Keywords: Chevalley groups, exceptional groups, width of a group, root elements
Received by editor(s): January 21, 2010
Published electronically: July 10, 2012
Additional Notes: This research was conducted in the framework of the joint project “Mikhail Lomonosov” of DAAD and Russian Ministry of Higher Education, and the RFBR project 09-01-00784-a.
Article copyright: © Copyright 2012 American Mathematical Society

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