UID:
almatuudk_9923185327902884
Format:
1 online resource (349 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88426-3
,
1-107-36626-7
,
1-107-37098-1
,
1-107-36135-4
,
1-107-36932-0
,
1-299-40405-7
,
1-107-36380-2
,
0-511-60065-8
Series Statement:
London Mathematical Society lecture note series ; 132
Content:
This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Title; Copyright; Preface; List of notation; Contents; Introduction; Historical survey; Algorithms for describing Wh(G); Survey of computations; Part I General theory; Chapter 1. Basic algebraic background; 1a. Orders in semi simple algebras; 1b. P-adic completion; 1c. Semi local rings and the Jacobson radical; 1d. Bimodule-induced homomorphisms and Morita equivalence; Chapter 2. Structure theorems for Ki of orders; 2a. Applications of the reduced norm; 2b. Logarithmic and exponential maps in p-adic orders; Chapter 3. Continuous K2 and localization sequences
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3a. Steinberg symbols in K2(R)3b. Continuous K2 of p-adic orders and algebras; 3c. Localization sequences for torsion in Whitehead groups; Chapter 4. The congruence subgroup problem; 4a. Symbols in K2 of p-adic fields; 4b. Continuous K2 of simple Qp-algebras; 4c. The calculation of C(Q[G]); Chapter 5 First applications of the congruence subgroup problem; 5a. Constructing and detecting elements in SKi: an example; 5b. Cl1(R[G]) and the complex representation ring; 5c. The standard involution on Whitehead groups; Chapter 6. The integral p-adic logarithm
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6a. The integral logarithm for p-adic group rings6b. Variants of the integral logarithm; 6c. Logarithms defined on Kc2(ZP[G]); Part II Group rings of p-groups; Chapter 7. The torsion subgroup of Whitehead groups; Chapter 8. The p-adic quotient of SK1(Z[G]): p-groups; 8a. Detection of elements; 8b. Establishing upper bounds; 8c. Examples; Chapter 9. Cl1(Z[G]) for p-groups; Chapter 10. The torsion free part of Wh(G); Part III General finite groups; Chapter 11. A quick survey of induction theory; 11a. Induction properties for Mackey functors and Green modules
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11b. Splitting p-local Mackey functorsChapter 12. The p-adic quotient of SK1(Z[G]): finite groups; Chapter 13. Cl1(Z[G]) for finite groups; 13a. Reduction to p-elementary groups; 13b. Reduction to p-groups; 13c. Splitting the inclusion Cl1(Z[G]) C SK1(Z[G]); Chapter 14. Examples; References; Index
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English
Additional Edition:
ISBN 0-521-33646-5
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9780511600654
