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Zap. Nauchn. Sem. POMI, 2014, Volume 423, Pages 183–204 (Mi znsl6004)  

This article is cited in 2 scientific papers (total in 2 papers)

Width of $\mathrm{GL}(6,K)$ with respect to quasi-root elements

I. M. Pevzner

Herzen State Pedagogical University of Russia, St. Petersburg, Russia

Abstract: We study structure of $\mathrm{GL}(6,K)$ with respect to a certain family of conjugacy classes, whose elements are called quasi-root. Namely, we prove that any element of $\mathrm{GL}(6,K)$ is a product of three quasi-root elements, and completely describe the elements that are products of two quasi-root elements. The result arises in the study of width of exceptional groups of type $E_6$, but also is of independent interest.

Key words and phrases: general linear group, width of group, root elements.

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English version:
Journal of Mathematical Sciences (New York), 2015, 209:4, 600–613

Bibliographic databases:

UDC: 512.5
Received: 15.09.2013

Citation: I. M. Pevzner, “Width of $\mathrm{GL}(6,K)$ with respect to quasi-root elements”, Problems in the theory of representations of algebras and groups. Part 26, Zap. Nauchn. Sem. POMI, 423, POMI, St. Petersburg, 2014, 183–204; J. Math. Sci. (N. Y.), 209:4 (2015), 600–613

Citation in format AMSBIB
\Bibitem{Pev14}
\by I.~M.~Pevzner
\paper Width of $\mathrm{GL}(6,K)$ with respect to quasi-root elements
\inbook Problems in the theory of representations of algebras and groups. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 423
\pages 183--204
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6004}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3480697}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 4
\pages 600--613
\crossref{https://doi.org/10.1007/s10958-015-2516-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84943448813}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. M. Pevzner, “Width of extraspecial unipotent radical with respect to root elements”, J. Math. Sci. (N. Y.), 219:4 (2016), 598–603  mathnet  crossref  mathscinet
    2. I. M. Pevzner, “Suschestvovanie kornevoi podgruppy, kotoruyu dannyi element perevodit v protivopolozhnuyu”, Voprosy teorii predstavlenii algebr i grupp. 32, Zap. nauchn. sem. POMI, 460, POMI, SPb., 2017, 190–202  mathnet
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