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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2015 Volume 435, Pages 168–177 (Mi znsl6156)

This article is cited in 4 papers

Width of extraspecial unipotent radical with respect to root elements

I. M. Pevzner

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

Abstract: Let $G=G(\Phi,K)$ be a Chevalley group of type $Ô$ over a field $K$, where $\Phi$ is a simply-laced root system. We study the extraspecial unipotent radical of $G$ and prove that any its element is a product of not more than three root elements. Moreover, we prove that any element of the radical is, possibly after a conjugation by an element of the Levi subgroup, a product of six elementary root elements.

Key words and phrases: Ñhevalley groups, extraspecial unipotent radical, width of group, root elements.

UDC: 512.5

Received: 01.10.2015


 English version:
Journal of Mathematical Sciences (New York), 2016, 219:4, 598–603

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© Steklov Math. Inst. of RAS, 2025