Mathematical Research Letters

Volume 10 (2003)

Number 5

On the surjectivity of the power maps of semisimple algebraic groups

Pages: 625 – 633

DOI: http://dx.doi.org/10.4310/MRL.2003.v10.n5.a6

Author

Pralay Chatterjee (Oklahoma State University)

Abstract

In this paper we study the surjectivity of the power maps $g\mapsto g^{n}$ for semisimple algebraic groups over an algebraically closed field of arbitrary characteristic. We describe certain necessary and sufficient conditions for surjectivity to hold. The results are applied to characterize the exponentiality of such groups.

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