Let formal multiplocative group be $$\mathbb{G}_m(X,Y) = X + Y + XY$$
Let $R$ be a complete local ring, and $M$ be its maximal ideal.
According to Silverman's 'the arithmetic of elliptic curves', group associated to formal multiplicative group, $\mathbb{G}_m(M) $ is $1＋M$ with group law multiplication.
But the book also reads group associated to formal groups $F（M）$ is $M$ as a set.
But $M$ and $1＋M$ is not the same set. What am I missing?