Mathematical Research Letters

Volume 9 (2002)

Number 6

On the surjectivity of the power maps of algebraic groups in characteristic zero

Pages: 741 – 756

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n6.a4

Author

Pralay Chatterjee (Tata Institute of Fundamental Research)

Abstract

In this paper we study the surjectivity of the power maps $g\mapsto g^{n}$ for algebraic groups over an algebraically closed field of characteristic zero. We describe certain necessary and sufficient conditions for surjectivity to hold, and using these results we determine the set of $n$ for which it holds in the case of simple algebraic groups. The results are also applied to study the exponentiality of algebraic groups.

Full Text (PDF format)