On the surjectivity of the power maps of algebraic groups in characteristic zero (Q1812519)

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.