On the orbit category on nontrivial $p$-subgroups and endotrivial
modules
On the orbit category on nontrivial $p$-subgroups and endotrivial
modules
Let $p$ be a prime, let $G$ be a finite group of order divisible by $p$, and let $k$ be a field of characteristic $p$. An endotrivial $kG$-module is a finitely generated $kG$-module $M$ such that its endomorphism algebra $\operatorname{End}_kM$ decomposes as the direct sum of a one-dimensional trivial $kG$-module …