Abstract
Let G be a finite group and k an algebraically closed field of characteristic \(p > 0\). Let \({\mathcal H}\) be a collection of p-subgroups of G. We investigate the relative stable category \(\mathbf{stmod}_{\mathcal H}(kG)\) of finitely generated modules modulo \({\mathcal H}\)-projective modules. Triangles in this category correspond to \({\mathcal H}\)-split sequences. Hence, compared to the ordinary stable category, there are fewer triangles and more thick subcategories. Our interest is in the spectrum of the category and its relationship to the induction functor. In some cases, the spectrum is not noetherian.
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