Exercise 27, § 1

Let $\mathbf{K}$ be a field of characteristic $p > 0$ and $G$ the 2-dimensional formal group defined by $f_1(\mathbf{x}, \mathbf{y}) = X_1 + Y_1 + X_1 Y_1, f_2(\mathbf{x}, \mathbf{y}) = X_2 + Y_2(1 + X_1^p).$ Show that $G$ is not commutative but that its Lie algebra is commutative.