Answer to Question #18661 in Abstract Algebra for john.george.milnor

Question

Let J be a nil ideal in an algebra R over a field k of characteristic 0, and let G be the group 1 + J ⊆ U(R). Similarly, show that two elements y, y' ∈ G commute iff log(y) and log(y') commute in J, in which case we have log(yy') = log(y) + log(y') ∈ J.