The strong Frobenius numbers for cyclic defect blocks are equal to one

TL;DR

This paper proves that the strong Frobenius number for blocks with cyclic defect groups in finite groups is always one, resolving a previously open question in the field.

Contribution

It establishes that the strong Frobenius number for cyclic defect blocks is equal to one, answering a question posed by Farrell and Kessar.

Findings

Strong Frobenius number for cyclic defect blocks is one

Provides a reference confirming the value for this class of blocks

Addresses an open question in modular representation theory

Abstract

The purpose of this note is to provide a reference for the fact that the strong Frobenius number, in the sense of Eaton and Livesey, of a block of a finite group with a cyclic defect group is equal to one. This answers a question of Farrell and Kessar.