Blocks of profinite groups with cyclic defect group

TL;DR

This paper proves that blocks of profinite groups with cyclic defect groups have a Brauer tree algebra structure similar to finite groups, with the Brauer tree being of star type for defect group rac{p}{}, extending known finite group results.

Contribution

It establishes the Brauer tree algebra structure for blocks of profinite groups with cyclic defect groups, generalizing finite group theory results.

Findings

Blocks with cyclic defect groups have Brauer tree algebra structure.

The Brauer tree for defect group rac{p}{ } is of star type.

Extension of finite group results to profinite groups.

Abstract

We demonstrate that the blocks of a profinite group whose defect groups are cyclic have a Brauer tree algebra structure analogous to the case of finite groups. We show further that the Brauer tree of a block with defect group $\mathbb{Z}_{p}$ is of star type.