A Witt-Burnside ring attached to a pro-dihedral group

TL;DR

This paper investigates a generalization of Witt vectors associated with a pro-dihedral group, analyzing the structure of the resulting ring in characteristic 2, extending classical Witt vector theory to new group contexts.

Contribution

It studies the structure of the Witt-Burnside ring for a pro-2 dihedral group, a novel case extending classical and known profinite group Witt vector theories.

Findings

Characterization of the Witt-Burnside ring for the pro-2 dihedral group

Insights into the ring's structure in characteristic 2

Extension of Witt vector theory to new profinite groups

Abstract

The ring of classic Witt vectors is a fundamental object in mixed characteristic commutative algebra which has many applications in number theory. There is a significant generalization due to Dress and Siebeneicher which for any profinite group G produces a ring valued functor W_G, where the classic Witt vectors are recovered as the example G = Z_p. This article explores the structure of the image of this functor where G is the pro-2 group formed by taking the inverse limit of 2-power dihedral groups, and the image of W_G is taken on a field of characteristic 2.