THICK SUBCATEGORIES OF THE RELATIVE STABLE CATEGORY
JON F. CARLSON
Abstract. Let G be a finite group and k an algebraically closed field of of char-
acteristic p > 0. Let H be a collection of p-subgroups of G. We investigate the
relative stable category stmodH(kG) of finitely generated modules modulo H-
projective modules. Triangles in this category correspond to 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 noether-
ian.