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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2024 Volume 531, Pages 147–151 (Mi znsl7447)

The existence of root subgroup translated by a given element into its opposite. II

I. M. Pevzner

Herzen State Pedagogical University of Russia, St. Petersburg

Abstract: Let $\Phi$ be a simply-laced root system, $|K|>5$, $G = G_{ad}(\Phi,K)$ the adjoint group of type $\Phi$ over $K$. Then for every non-trivial element $g\in G$ there exists a root element $x$ of the Lie algebra of $G$ such that $x$ and $gx$ are opposite.

Key words and phrases: Ñhevalley groups, root elements.

UDC: 512.5

Received: 22.04.2024



© Steklov Math. Inst. of RAS, 2025