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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 413, Pages 93–105 (Mi znsl5657)  

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

Commutators with some special elements in Chevalley groups

N. Gordeeva, E. W. Ellersb

a Russian State Pedagogical University, Moijka 48, 191186 St. Petersburg, Russia
b Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
Full-text PDF (235 kB) Citations (2)
References:
Abstract: Let $G=\widetilde G(K)$ where $\widetilde G$ is a simple and simply connected algebraic group that is defined and quasi-split over a field $K$. We consider commutators in $G$ with some regular elements. In particular, we prove (under some additional condition) that every unipotent regular element of $G$ is conjugate to a commutator $[g,v]$, where $g$ is any fixed semisimple regular element of $G$, and that every non-central element of $G$ is conjugate to a product $[g,\sigma][u_\mathrm{reg},\tau]$, where $g$ is some special element of the group $G$ and $u_\mathrm{reg}$ is some regular unipotent element of $G$.
Key words and phrases: commutators in Chevalley groups, regular elements in Chevalley groups, the Ore's problem.
Received: 16.04.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 202, Issue 3, Pages 395–403
DOI: https://doi.org/10.1007/s10958-014-2049-y
Bibliographic databases:
Document Type: Article
UDC: 512.743
Language: English
Citation: N. Gordeev, E. W. Ellers, “Commutators with some special elements in Chevalley groups”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 93–105; J. Math. Sci. (N. Y.), 202:3 (2014), 395–403
Citation in format AMSBIB
\Bibitem{GorEll13}
\by N.~Gordeev, E.~W.~Ellers
\paper Commutators with some special elements in Chevalley groups
\inbook Problems in the theory of representations of algebras and groups. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 413
\pages 93--105
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5657}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073059}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 3
\pages 395--403
\crossref{https://doi.org/10.1007/s10958-014-2049-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919920074}
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  • https://www.mathnet.ru/eng/znsl/v413/p93
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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