I am reading Formal groups, Lubin Tate formal groups from Milne's class field theory notes.
I understand that group law on a commutative ring is a power series expansion in two variables with some conditions.
Let $K$ be a local field and $A$ be its ring of integers. Let $\pi$ be a uniformizer of $A$ then we have a subcollection $\mathfrak{F}_{\pi}$ of power series in one variable $T$. It then gives some groups laws related to the set defined above. I do not see where we are leading to.
It would be great if some one can give some reference for an article on formal groups just like What is Reciprocity law article by Wyman for Reciprocity laws.
Well, I suppose the important fact about a formal group law over $A$ is that it turns the maximal ideal $\mathfrak M$ in the integers of each finite extension $L\supset K$ into a group that’s a Galois module. Being suitably careful, you can even let $L$ be an infinite complete extension of $K$. In any case, this group may be very different indeed from the additive group $\mathfrak M^+$ and from the multiplicative group $1+\mathfrak M$. In particular, its torsion subgroup may give a very useful representation module for the Galois group.
Keep on reading. I can’t imagine that there are many better expositors than Milne, but people tell me that the original L-T paper is very readable. It seems to be available on JSTOR.