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Modules (Algebra) --- Endomorphism rings --- Direct sum decompositions
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Multichip modules (Microelectronics) --- Microelectronic packaging --- Congresses
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This book provides a detailed but concise account of the theory of structure of finite p-groups admitting p-automorphisms with few fixed points. The relevant preliminary material on Lie rings is introduced and the main theorems of the book on the solubility of finite p-groups are then presented. The proofs involve notions such as viewing automorphisms as linear transformations, associated Lie rings, powerful p-groups, and the correspondences of A. I. Mal'cev and M. Lazard given by the Baker-Hausdorff formula. Many exercises are included. This book is suitable for graduate students and researchers working in the fields of group theory and Lie rings.
Automorphisms. --- Finite groups. --- Groups, Finite --- Group theory --- Modules (Algebra) --- Symmetry (Mathematics)
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Ordered algebraic structures --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra)
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Linear algebraic groups --- Geometry, Algebraic --- 512.7 --- 512.55 --- 512.5 --- Algebraic geometry. Commutative rings and algebras --- Rings and modules --- General algebra --- 512.5 General algebra --- 512.55 Rings and modules --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic groups, Linear --- Group theory --- Algebraic varieties --- Algebraic geometry --- Geometry --- Groupes algébriques linéaires --- Geometrie algebrique --- Groupes algebriques
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This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.
Finite groups. --- Characters of groups. --- Blocks (Group theory) --- Block theory (Group theory) --- Representations of groups --- Characters, Group --- Group characters --- Groups, Characters of --- Finite groups --- Rings (Algebra) --- Groups, Finite --- Group theory --- Modules (Algebra)
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Computer software --- Object-oriented programming (Computer science) --- Software patterns --- 681.3*D22 --- 681.3*D22 Tools and techniques: decision tables; flow charts; modules and interfaces; programmer workbench; software libraries; structured programming; top-down programming; user interfaces (Software engineering) --- Tools and techniques: decision tables; flow charts; modules and interfaces; programmer workbench; software libraries; structured programming; top-down programming; user interfaces (Software engineering) --- Patterns, Software --- Computer programming --- Object-oriented methods (Computer science) --- Document Object Model (Web site development technology) --- Development of computer software --- Software development --- Development --- Computer. Automation --- Object-oriented programming (Computer science). --- Software patterns. --- Development.
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