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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2013 Volume 413, Pages 93–105 (Mi znsl5657)

This article is cited 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.

UDC: 512.743

Received: 16.04.2013

Language: English


 English version:
Journal of Mathematical Sciences (New York), 2014, 202:3, 395–403

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