On the extension giving the truncated Witt vectors

Abstract

We explore the theory of cohomology of groups and the classification of group extensions with abelian kernel. We then look at the group extensions that underlie the truncated Witt vectors on the truncation set {1,p} where p is a prime number. It turns out that we can do without the multiplicative structure on the source ring A by factoring the extension's representing cocycle through a map into the p-fold tensor product of A divided out by the C_p-action.