Group Algebras of pro-p Groups

Abstract

The results to be proved in this chapter refer again mostly to presentations of a pro-p group by generators and relations. They will be derived using the complete group algebra of a pro-p group. In this chapter, Λ will always denote a compact commutative ring with identity. For finite groups G, the additive group of the group ring Λ[G] is isomorphic to the direct sum of #G copies of Λ, and thus inherits a topology that makes Λ[G] into a compact group ring.