ABSTRACT
This chapter discusses the decomposition theorem, the structure of linearly compact algebras over a perfect field, and infinitesimal formal groups. It mentions only a few properties of the etale formal groups. The structure theorem for stable infinitesimal formal groups is described. The chapter describes stable bigebras and reduced formal groups along with reduced infinitesimal formal groups. The stable invariant subbigebras of a reduced bigebra is characterized based on the infinitesimal formal groups. The elementary theory of reduced infinitesimal groups cannot be developed as simply as the classical theory of groups. This leads to introduce new notions for reduced groups of finite dimension.
