Invariant blocks under coprime actions

TL;DR

This paper establishes a precise correspondence between A-invariant Brauer p-blocks of a finite group G and A-invariant irreducible characters when a finite group A acts coprimely on G.

Contribution

It provides a clear characterization of A-invariant blocks in terms of invariant characters under coprime automorphism actions.

Findings

A-invariant Brauer p-blocks correspond exactly to A-invariant irreducible characters.

The result applies to coprime automorphism actions on finite groups.

This characterization simplifies understanding of block invariance under automorphisms.

Abstract

If a finite group $A$ acts coprimely as automorphisms on a finite group $G$, then the $A$-invariant Brauer $p$-blocks of $G$ are exactly those that contain $A$-invariant irreducible characters.