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AuthorHuppert, Bertram. author
TitleFinite Groups II [electronic resource] / by Bertram Huppert, Norman Blackburn
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1982
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Descript XIV, 534 p. online resource


17):̃t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From "Lohengrin", Richard Wagner At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made it virtually impossible to give a complete presentation of the subject in one treatise. The present volume and its successor have therefore the more modest aim of giving descriptions of the recent development of certain important parts of the subject, and even in these parts no attempt at completeness has been made. Chapter VII deals with the representation theory of finite groups in arbitrary fields with particular attention to those of non-zero characยญ teristic. That part of modular representation theory which is essentially the block theory of complex characters has not been included, as there are already monographs on this subject and others will shortly appear. Instead, we have restricted ourselves to such results as can be obtained by purely module-theoretical means


VII. Elements of General Representation Theory -- ยง 1. Extension of the Ground-Field -- ยง 2. Splitting Fields -- ยง 3. The Number of Irreducible Modular Representations -- ยง 4. Induced Modules -- ยง 5. The Number of Indecomposable KG-Modules -- ยง 6. Indecomposable and Absolutely Indecomposable Modules -- ยง 7. Relative Projective and Relative Injective Modules -- ยง 8. The Dual Module -- ยง 9. Representations of Normal Subgroups -- ยง10. One-Sided Decompositions of the Group-Ring -- ยง11. Frobenius Algebras and Symmetric Algebras -- ยง12. Two-Sided Decompositions of Algebras -- ยง13. Blocks of p-Constrained Groups -- ยง14. Kernels of Blocks -- ยง15. p-Chief Factors of p-Soluble Groups -- ยง16. Greenโ{128}{153}s Indecomposability Theorem -- Notes on Chapter VII -- VIII. Linear Methods in Nilpotent Groups -- ยง 1. Central Series with Elementary Abelian Factors -- ยง 2. Jenningsโ{128}{153} Theorem -- ยง 3. Transitive Linear Groups -- ยง 4. Some Number-Theoretical Lemmas -- ยง 5. Lemmas on 2-Groups -- ยง 6. Commutators and Bilinear Mappings -- ยง 7. Suzuki 2-Groups -- ยง 8. Lie Algebras -- ยง 9. The Lie Ring Method and an Application -- ยง10. Regular Automorphisms -- ยง11. The Lower Central Series of Free Groups -- ยง12. Remarks on the Burnside Problem -- ยง13. Automorphisms of p-Groups -- Notes on Chapter VIII -- IX. Linear Methods and Soluble Groups -- ยง1. Introduction -- ยง2. Hall and Higmanโ{128}{153}s Theorem B -- ยง3. The Exceptional Case -- ยง4. Reduction Theorems for Burnsideโ{128}{153}s Problem -- ยง5. Other Consequences of Theorem B -- ยง6. Fixed Point Free Automorphism Groups -- ยง7. p-Stability -- ยง8. Soluble Groups with One Class of Involutions -- Notes on Chapter IX -- Index of Names

Mathematics Group theory Mathematics Group Theory and Generalizations


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