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The Auslander-Reiten quiver of a finite group

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References

  1. Alperin, J.L.: Periodicity in groups. Illinois J. Math.21, 776–783 (1977)

    Google Scholar 

  2. Alperin, J.L., Evens, L.: Representations, resolutions and Quillen's dimension theorem. J. Pure Appl. Algebra22, 1–10 (1981)

    Google Scholar 

  3. Atiyah, M.F., Macdonald, I.G.: Introduction to Commutative Algebra. Reading, Massachusetts: Addison-Wesley 1969

    Google Scholar 

  4. Auslander, M.: Applications of morphisms determined by objects. In: Proceedings of a Conference on Representation Theory of Algebras Philadelphia 1976, pp. 245–327. New York-Basel: Marcel Dekker 1978

    Google Scholar 

  5. Auslander, M.: Existence theorems for almost split sequences. In: Ring Theory II. Proceedings of the Second Oklahoma Conference (Norman, Oklahoma 1975), pp. 1–44. New York-Basel: Marcel Dekker 1977

    Google Scholar 

  6. Auslander, M., Reiten, I.: Representation theory of artin algebras IV: Invariants given by almost split sequences. Comm. Algebra5, 443–518 (1977)

    Google Scholar 

  7. Auslander, M., Reiten, I.: Representation theory of artin algebras V: Methods for computing almost split sequences and irreducible morphisms. Comm. Algebra5, 519–544 (1977)

    Google Scholar 

  8. Auslander, M., Reiten, I.: Uniserial functors. In: Representation Theory II. Proceedings of a Conference (Ottawa 1979), pp. 1–47. Lecture Notes in Mathematics832, Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  9. Benson, D., Parker, R.A.: The Green ring of a finite group. Preprint

  10. Blackburn, N.: Generalization of certain elementary theorems onp-groups. Proc. Lond. Math. Soc. (3)11, 1–22 (1961)

    Google Scholar 

  11. Butler, M.C.R., Shahzamanian, M.: The construction of almost split sequences, III: Modules over two classes of tame local algebras, Math. Ann.247, 111–122 (1980)

    Google Scholar 

  12. Cartan, H., Eilenberg, S.: Homological Algebras. Princeton, N.J.: Princeton University Press 1956

    Google Scholar 

  13. Chouinard L.G.: Projectivity and relative projectivity over group rings. J. Pure Appl. Algebra7, 278–302 (1976)

    Google Scholar 

  14. Dlab, V., Ringel, C.M.: Indecomposable representations of graphs and algebras. Mem. Amer. Math. Soc.173 (1976)

  15. Eisenbud, D.: Homological algebra on a complete intersection, with an application to group representations. Trans. Amer. Math. Soc.261, 35–64 (1980)

    Google Scholar 

  16. Erdmann, K.: Principal 2-blocks of groups with dihedral Sylow 2-subgroups. Comm. Algebra5, 665–694 (1977)

    Google Scholar 

  17. Gabriel, P.: Auslander-Reiten sequences and representation-finite algebras. In: Representation Theory I. Proceedings of a Conference (Ottawa 1979), pp. 1–71. Lecture Notes in Mathematics831, Berlin-Heidelber-New York: Springer 1980

    Google Scholar 

  18. Gabriel, P., Riedtmann, C.: Group representations without groups. Comment. Math. Helv.54, 240–287 (1979)

    Google Scholar 

  19. Green, J.A.: Vorlesungen über modulare Darstellungstheorie endlicher Gruppen. Vorlesungen aus dem Mathematischen Institut Giessen, Heft2 (1974)

  20. Gruenberg, K.W.: Cohomological topics in group theory, Lecture Notes in Mathematics143. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  21. Happel, D., Preiser, U., Ringel, C.M.: Vinberg's characterization of Dynkin diagrams using subadditive functions with application toDTr-periodic modules. In: Representation Theory II. Proceedings of a Conference (1979) pp. 280–294, Lecture Notes in Mathematics832, Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  22. Jennings, S.A.: The structure of the group ring of ap-group over a modular field. Trans. Amer. Math. Soc.50, 175–185 (1941)

    Google Scholar 

  23. Riedtmann, C.: Algebren, Darstellungsköcher, Überlagerungen und zurück, Comment. Math. Helv.55, 199–224 (1980)

    Google Scholar 

  24. Riedtmann, C.: Representation-finite selfinjective algebras of classA n. In: Representation Theory II. Proceeding of a Conference (1979), pp. 449–520. Lecture Notes in Mathematics832. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  25. Ringel, C.M.: Report on the Brauer-Thrall conjectures: Roiter's theorem and the theorem of Nazarova and Roiter. In: Representation Theory I. Proceedings of a Conference (Ottawa 1979), pp. 104–136. Lecture Notes in Mathematics831. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  26. Roggenkamp, K.W.: Lattices over Orders II. Lecture Notes in Mathematics142. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  27. Roggenkamp, K.W.: The construction of almost split sequences for integral group rings and orders. Comm. Algebra5, 1363–1373 (1977)

    Google Scholar 

  28. Roggenkamp, K.W.: Integral representations and structure of finite group rings. Montreal: Les Presses de l'Université de Montréal 1980

    Google Scholar 

  29. Talelli, O.: On cohomological periodicity of ℤG-lattices. Math. Z.169, 119–126 (1979)

    Google Scholar 

  30. Wiedemann, A.: Orders with loops in their Auslander-Reiten graph. Comm. Algebra9, 641–656 (1981)

    Google Scholar 

  31. Reiten, I.: Almost split sequences for group algebras of finite representation type. Trans. Amer. Math. Soc.233, 125–136 (1977)

    Google Scholar 

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Webb, P.J. The Auslander-Reiten quiver of a finite group. Math Z 179, 97–121 (1982). https://doi.org/10.1007/BF01173918

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