By using the method of Markov-Kakutani fixed point theorem, it is proved that Z(superscript d) action on compact groups by rotation is topologically transitive if and only if it is ergodic.

• 利用Markov-Kakutani不动点定理证明了紧群上的Z(上标 d)左平移作用是拓扑可迁的当且仅当是遍历的。