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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 413, Pages 93–105
(Mi znsl5657)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl5657 https://www.mathnet.ru/eng/znsl/v413/p93
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Abstract page: | 227 | Full-text PDF : | 36 | References: | 40 |
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