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Finite Group Algebras and their Modules

Finite Group Algebras and their Modules


Part of London Mathematical Society Lecture Note Series

  • Date Published: December 1983
  • availability: Available
  • format: Paperback
  • isbn: 9780521274876

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About the Authors
  • Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.

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    Product details

    • Date Published: December 1983
    • format: Paperback
    • isbn: 9780521274876
    • length: 286 pages
    • dimensions: 229 x 152 x 16 mm
    • weight: 0.43kg
    • availability: Available
  • Table of Contents

    Part I. The Structure of Group Algebras:
    1. Idempotents in rings. Liftings
    2. Projective and injective modules
    3. The radical and artinian rings
    4. Cartan invariants and blocks
    5. Finite dimensional algebras
    6. Duality
    7. Symmetry
    8. Loewy series and socle series
    9. The p. i. m.'s
    10. Ext
    11. Orders
    12. Modular systems and blocks
    13. Centers
    14. R-forms and liftable modules
    15. Decomposition numbers and Brauer characters
    16. Basic algebras and small blocks
    17. Pure submodules
    18. Examples
    Part II. Indecomposable Modules and Relative Projectivity:
    1. The trace map and the Nakayama relations
    2. Relative projectivity
    3. Vertices and sources
    4. Green Correspondence
    5. Relative projective homomorphisms
    6. Tensor products
    7. The Green ring
    8. Endomorphism rings
    9. Almost split sequences
    10. Inner products on the Green ring
    11. Induction from normal subgroups
    12. Permutation models
    13. Examples
    Part III. Block Theory:
    1. Blocks, defect groups and the Brauer map
    2. Brauer's First Main Theorem
    3. Blocks of groups with a normal subgroup
    4. The Extended First main Theorem
    5. Defect groups and vertices
    6. Generalized decomposition numbers
    7. Subpairs
    8. Characters in blocks
    9. Vertices of simple modules
    10. Defect groups

  • Author

    P. Landrock

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