Centralizers in good groups are good

TL;DR

This paper enhances transchromatic character maps using algebraic and topological localization techniques, demonstrating that centralizers of certain elements in good groups retain goodness and providing new computational examples.

Contribution

It introduces a modified transchromatic character map framework and proves centralizers of prime-power order elements in good groups are also good, with new computational insights.

Findings

Centralizers of prime-power order elements are good

New example of a good group computed

Modified character maps using localization techniques

Abstract

We modify the transchromatic character maps to land in a faithfully flat extension of Morava E-theory. Our construction makes use of the interaction between topological and algebraic localization and completion. As an application we prove that centralizers of tuples of commuting prime-power order elements in good groups are good and we compute a new example.