The Brauer indecomposability of Scott modules and the quadratic group Qd(p)

Abstract

Let $k$ be an algebraically closed field of prime characteristic $p$ and $P$ a finite $p$-group. We compute the Scott $kG$-module with vertex $P$ when $\mathcal{F}$ is a constrained fusion system on $P$ and $G$ is Park's group for $\mathcal{F}$. In the case $\mathcal{F}$ is a fusion system of the quadratic group $Qd(p)=(\mathbb{Z}/p\times \mathbb{Z}/p)⋊\mathrm{SL}(2,p)$ on a Sylow $p$-subgroup $P$ of $Qd(p)$ and $G$ is Park's group for $\mathcal{F}$, we prove that the Scott $kG$-module with vertex $P$ is Brauer indecomposable.

arXiv commentTo appear in Algebras and Representation Theory

Cited by in corpus (2)

• The Brauer indecomposability of Scott modules with semidihedral vertex
• The Brauer indecomposability of Scott modules with wreathed $2$-group vertices