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Thursday, July 30, 2020 | History

3 edition of **Induction theorems for Grothendieck groups and Whitehead groups of finite groups** found in the catalog.

Induction theorems for Grothendieck groups and Whitehead groups of finite groups

T. Y. Lam

- 222 Want to read
- 36 Currently reading

Published
**1967**
by Columbia University in [New York]
.

Written in English

- Grothendieck groups.,
- Whitehead groups.,
- Induction (Mathematics)

**Edition Notes**

Statement | by Tsit-Yuen Lam. |

Classifications | |
---|---|

LC Classifications | QA171 .L275 |

The Physical Object | |

Pagination | 146 l. |

Number of Pages | 146 |

ID Numbers | |

Open Library | OL3899455M |

LC Control Number | 81461543 |

(e.g. Ro theorem , Navarro 03) for cyclic groups e.g. (Alu pages ) This is a special case of the structure theorem for finitely generated modules over a principal ideal domain.. Examples. The following examples may be useful for illustrative or instructional purposes. Book digitized by Google and uploaded to the Internet Archive by user tpb. "An unabridged republication of the second edition, published in "Pages:

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share . In this regard, the book reads at times less like a textbook and more like a novel on the great narrative of the story of the development of finite group theory over the last twelve decades. The running theme unifying all these results in the narrative is the great accomplishment of the classification of finite simple groups.

Dually a co-Grothendieck category is an AB5 * ^* category with a cogenerator. The category of abelian groups is not a co-Grothendieck category. Any abelian category which is simultaneously Grothendieck and co-Grothendieck has just a single object (see Freyd’s book, p). Properties. A Grothendieck category C C satisfies the following. IntroductionGAPDecomposing groupsFinite simple groupsExtension theoryNilpotent groupsFinite p-groupsEnumeration of nite groups Sylow theorems Basic structure of nite groups Theorem (Sylow’s theorems) Let G be a group of order pa m, where m is not divisible by the prime p. Then the following holds: 1 G contains at least one subgroup of order.

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[15] T. LAM, Induction Theorems for Grothendieck Groups and Whitehead Groups of Finite Groups, Ann. Sci. Ecole Norm. Sup. 4e serie 1 (), [16] J. LEICHT and F. LORENZ, Die Primideale. Induction for finite groups is a general method, or collection of methods, aimed to prove that a certain result holds true for all finite groups (or for an infinite collection of finite groups).

While this uses the same principle of mathematical induction that characterizes the usual application of induction, the way the principle is applied is. T.-Y. Lam, Induction theorems for Grothendieck groups and Whitehead groups of finite groups, Ann.

Norm. Sup. 1 (4) () [6] T. torn Dieck, Transformation groups and representation theory, Lecture Notes in Mathematics, Vol.

(Springer, New York, ).Cited by: History. During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence, the complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be built are now known.

With applications to finite groups and orders Charles W. Curtis, Irving Reiner. Categories: Mathematics\\Symmetry and group.

induction formula proposition integral Post a Review You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

Lam, Induction theorems for Grothendieck groups and Whitehead groups of finite groups, Ann. sci. Ecole norm. sup. Ser. 1,91– MathSciNet zbMATH Cited by: 1. In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic.

Group theory is central to many areas of pure and applied mathematics and the classification. Definition. An A-group is a finite group with the property that all of its Sylow subgroups are abelian. History. The term A-group was probably first used in (HallSec.

9), where attention was restricted to soluble 's presentation was rather brief without proofs, but his remarks were soon expanded with proofs in ().The representation theory of A-groups was studied in (). thereby giving representations of the group on the homology groups of the space.

If there is torsion in the homology these representations require something other than ordinary character theory to be understood. This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract Size: 1MB.

For smooth varieties over finite fields, we prove that the shifted (aka derived) Witt groups of surfaces are finite and the higher Grothendieck–Witt groups (aka Hermitian K-theory) of curves are finitely more general arithmetic schemes, we give conditional results, for example, finite generation of the motivic cohomology groups implies finite generation of the Grothendieck Cited by: 4.

T. Lam, Induction theorems for Grothendieck groups and Whitehead groups of finite groups, Ann. Sci. École Norm. Sup., 4 e série 1(), 99– MathSciNet Google Scholar [11]Cited by: 3. X= [D2D D. Corollary If R is an equivalence relation on a set X, then D R= fR[x]: x2Xg is a disjoint partition of X.

Theorem Let D be a disjoint partition of a set X. De ne a relation on X, RFile Size: KB. The "Theory of Groups of Finite Order" by Burnside was first published in and a second edition in ; the Dover Phoenix edition is a reprint of the second edition.

The book can be considered as a milestone in the theory of groups/5(4). This book is a short introduction to the subject, written both for beginners and for mathematicians at large. There are ten chapters: Preliminaries, Sylow theory, Solvable groups and nilpotent groups, Group extensions, Hall subgroups, Frobenius groups, Transfer, Characters, Finite subgroups of Cited by: On relative Grothendieck rings.

Induction theorems for Grothendieck groups and Whitehead groups of finite groups. for finite groups pi. In this setting, the crucial (and most subtle Author: Andreas Dress.

December This article is the winner of the general public category of the Plus new writers award Daniel Gorenstein "In February the classification of finite simple groups was completed." So wrote Daniel Gorenstein, the overseer of the programme behind this classification: undoubtedly one of the most extraordinary theorems that pure mathematics has ever seen.

How to Cite This Entry: Grothendieck group. Encyclopedia of Mathematics. URL: ?title=Grothendieck_group&oldid= too closely at the general finite group, but instead when faced with a problem about finite groups, to attempt to reduce the problem or a related prob-lem to a question about simple groups or groups closely related to simple groups.

Then using the Classification of the finite simple groups and knowl-edge of the simple groups, solve the reduced. Product of two groups 26 Induced representations 28 4 Compact groups 32 4.) Compact groups 32 Invariant measure on a compact group 32 Linear representations of compact groups ~, 33 vii.

Resources Online textbooks:Representation Theory Book We need the first 5 sections (pages ).Representations of finite groups ta, Notes on representations of algebras and finite groups n, Notes on the representation theory of finite groups f et al. Introduction to representation theory also discusses category theory, Dynkin diagrams, and.

Preview this book» What people are Theorems of Galois Jordan Holder. CHAPTER III. Theory and Applications of Finite Groups George Abram Miller, Hans Frederick Blichfeldt, Leonard Eugene Dickson Full view - THEORY AND APLICATIONS OF FINITE GROUPS G.A.

MILLER,H.F. BLICHFELDT.Groups similar to Galois groups are called permutation groups these days. This concept was investigated by Augustine-Louis Cauchy, and was re ned by Arthur Cayley in Number theory (Carl Friedrich Gauss, ): The second root to the Finite Groups theory is Number theory.

This theory was presented by C. F. Gauss in his paper \Disquisitones.Rather than studying arbitrary simple groups, the effort is currently centered on those simple groups that have finite Morley rank, a certain generalization of the idea of dimension.

This finite dimensionality assumption has proved very fruitful in terms of lifting and generalizing techniques from .