Frobenius Categories versus Brauer Blocks

1. Introduction

2. General notation and quoted results

3. Frobenius P-categories: the first definition

4. The Frobenius P-category of a block

5. Nilcentralized, selfcentralizing and intersected objects in Frobenius P-categories

6. Alperin fusions in Frobenius P-categories

7. Exterior quotient of a Frobenius P-category over the selfcentralizing objects

8. Nilcentralized and selfcentralizing Brauer pairs in blocks

9. Decompositions for Dade P-algebras

10. Polarizations for Dade P-algebras

11. A gluing theorem for Dade P-algebras

12. The nilcentralized chain k*-functor of a block

13. Quotients and normal subcategories in Frobenius P-categories

14. The hyperfocal subcategory of a Frobenius P-category

15. The Grothendieck groups of a Frobenius P-category

16. Reduction results for Grothendieck groups

17. The local-global question: reduction to the simple groups

18. Localities associated with a Frobenius P-category

19. The localizers in a Frobenius P-category

20. Solvability for Frobenius P-categories

21. A perfect F-locality from a perfect Fsc -locality

22. Frobenius P-categories: the second definition

23. The basic F-locality

24. Narrowing the basic Fsc-locality

25. Looking for a perfect Fsc-locality

Nyckelord: Mathematics, Group Theory and Generalizations, Algebraic Topology