Kernel of Scott modules and Brauer indecomposability

TL;DR

This paper studies the Brauer indecomposability of Scott modules over finite groups, providing a generalized criterion and conditions for lifting indecomposability from subgroups.

Contribution

It generalizes a criterion for Brauer indecomposability and establishes conditions for lifting indecomposability from p-local subgroups.

Findings

Generalized criterion for Brauer indecomposability

Lifting of indecomposability from p-local subgroups in certain cases

Enhanced understanding of kernel relations in Scott modules

Abstract

Let $k$ be an algebraically closed field of a prime characteristic $p$. Let $G$ be a finite group. We investigate the Brauer indecomposability of Scott $kG$-modules in relation to the kernel of modules. We generalize a criterion for Brauer indecomposability. We also prove that, in certain cases, Brauer indecomposability of a Scott $kG$-module can be lifted from that of a Scott module over a $p$-local subgroup.