On the surjectivity of the power maps of algebraic groups in characteristic zero
type: Item
instance of: scholarly article
title: On the surjectivity of the power maps of algebraic groups in characteristic zero
zbMATH Open document ID: 1025.20034
author: Pralay Chatterjee
published in: Mathematical Research Letters
publication date: 2003-09-17T00:00:00Z
review text: Let \(G\) be an algebraic group over an algebraically closed field of characteristic zero. For a natural number \(n\), let \(P_n\colon G\to G\) be the \(n\)-th power map defined by \(P_n(g)=g^n\). The author gives some necessary and sufficient conditions under which the power map \(P_n\) is surjective, and determines the set of \(n\) for which surjectivity holds in the case of simple algebraic groups. The author also studies the exponentiality of algebraic groups.
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1930994
zbMATH Keywords: algebraic groups
zbMATH Keywords: power maps
zbMATH Keywords: surjectivity
zbMATH Keywords: exponentiality
MaRDI profile type: Publication
full work available at URL: mrl.2002.v9.n6.a4
OpenAlex ID: W2061175295
DOI: 10.4310/MRL.2002.V9.N6.A4
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description: scientific article; zbMATH DE number 1930994