  The classical Witt vectors are a ubiquitous object in algebra and number
theory. They arise as a functorial construction that takes perfect fields k of
prime characteristic p > 0 to p-adically complete discrete valuation rings of
characteristic 0 with residue field k and are universal in that sense. A. Dress
and C. Siebeneicher generalized this construction by producing a functor W_G
attached to any profinite group G. The classical Witt vectors are those
attached to the p-adic integers. Here we examine the ring structure of W_G(k)
for several examples of pro-p groups G and fields k of characteristic p. We
will show that the structure is surprisingly more complicated than the
classical case.
