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.
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Generalov, A.I., Isametdinov, I.O. Decomposition of the Grothendieck Group of Stable Categories of Finite Groups. Journal of Mathematical Sciences 112, 4333–4336 (2002). https://doi.org/10.1023/A:1020390818802
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DOI: https://doi.org/10.1023/A:1020390818802