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Zap. Nauchn. Sem. POMI, 2011, Volume 394, Pages 20–32 (Mi znsl4629)  

$\mathrm{SL}_2$-factorisations of Chevalley groups

N. A. Vavilov, E. I. Kovach

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: Recently Liebeck, Nikolov, and Shalev noticed that finite Chevalley groups admit fundamental $\mathrm{SL}_2$-factorizations of length $5N$, where $N$ is the number of positive roots. From a recent paper by Smolensky, Sury, and Vavilov it follows that elementary Chevalley groups over rings of stable rank 1 admit such factorizations of length $4N$. In the present paper, we establish two further improvements of these results. Over any field the bound here can be improved to $3N$. On the other hand, for $\mathrm{SL}(n,R)$, over a Bezout ring $R$, we further improve the bound to $2N=n^2-n$.

Key words and phrases: Chevalley groups, fundamental $\mathrm{SL}_2$, semisimple factorisations, Bezout rings, parabolic subgroups, bounded generation.

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English version:
Journal of Mathematical Sciences (New York), 2013, 188:5, 483–489

Bibliographic databases:

Document Type: Article
UDC: 512.5
Received: 30.06.2011

Citation: N. A. Vavilov, E. I. Kovach, “$\mathrm{SL}_2$-factorisations of Chevalley groups”, Problems in the theory of representations of algebras and groups. Part 22, Zap. Nauchn. Sem. POMI, 394, POMI, St. Petersburg, 2011, 20–32; J. Math. Sci. (N. Y.), 188:5 (2013), 483–489

Citation in format AMSBIB
\Bibitem{VavKov11}
\by N.~A.~Vavilov, E.~I.~Kovach
\paper $\mathrm{SL}_2$-factorisations of Chevalley groups
\inbook Problems in the theory of representations of algebras and groups. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 394
\pages 20--32
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4629}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2870171}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 5
\pages 483--489
\crossref{https://doi.org/10.1007/s10958-013-1145-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884414794}


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