Every smooth p-adic Lie group admits a compatible analytic structure

We show that every finite-dimensional p-adic Lie group of class C-k (where k is an element of N boolean OR {infinity}) admits a C-k-compatible analytic Lie group structure. We also construct an exponential map for every k + 1 times strictly differentiable (SCk+1) ultrametric p-adic Banach-Lie group, which is an SC1-diffeomorphism and admits Taylor expansions of all finite orders <= k.