Decomposition of the Grothendieck group of stable categories of finite groups.

Abstract

Let G be a finite group with a normal Sylow p-subgroup H such that the corresponding quotient is Abelian. We prove that the Grothendieck group of the stable category of G (over an algebraically closed field of characteristic p) contains a cyclic direct summand of order \(\left| H \right|\). Bibliography: 6 titles.