On power maps in algebraic groups.
type: Item
instance of: scholarly article
title: On power maps in algebraic groups.
zbMATH Open document ID: 1045.20044
author: Robert Steinberg
published in: Mathematical Research Letters
publication date: 2004-05-18T00:00:00Z
review text: Let \(K\) be a field of characteristic exponent \(p\). (So if \(p=1\) then \(K\) has characteristic zero and otherwise it has characteristic \(p\).) The goal of this short note is to prove: Let \(G\) be a (connected) semisimple algebraic group over \(K\) and \(n\) a positive integer which is prime to \(p\). Then the power map \(P_n\) on \(G\) defined by \(x\mapsto x^n\) is surjective if and only if \(n\) is prime to the bad primes for \(G\) and also to the central primes, those that divide the order of the center of \(G\). This removes the restriction to characteristic zero in theorem C of \textit{P. Chatterjee} [Math. Res. Lett. 9, No. 5-6, 741-756 (2002; Zbl 1025.20034)]. -- See also the preceding review Zbl 1045.20043.
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 2064718
zbMATH Keywords: bad primes
zbMATH Keywords: power maps
zbMATH Keywords: exponential algebraic groups
MaRDI profile type: Publication
DOI: 10.4310/MRL.2003.V10.N5.A5
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description: scientific article; zbMATH DE number 2064718