Arithmetical Similarities: Prime Decomposition and Finite Group Theory

Hardcover | April 30, 1998

byN. Klingen

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This book deals with the characterization of extensions of number fields in terms of the decomposition of prime ideals, and with the group-theoretic questions arising from this number-theoretic problem. One special aspect of this question is the equality of Dedekind zeta functions ofdifferent number fields. This is an established problem which was solved for abelian extensions by class field theory, but which was only studied in detail in its general form from around 1970. The basis for the new results was a fruitful exchange between number theory and group theory. Some ofthe outstanidng results are based on the complete classification of all finite simple groups. This book reports on the great progress achieved in this period. It allows access to the new developments in this part of algebraic number theory and contains a unique blend of number theory and grouptheory. The results appear for the first time in a monograph and they partially extend the published literature.

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This book deals with the characterization of extensions of number fields in terms of the decomposition of prime ideals, and with the group-theoretic questions arising from this number-theoretic problem. One special aspect of this question is the equality of Dedekind zeta functions ofdifferent number fields. This is an established pro...

N. Klingen is at University of Cologne.

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Format:HardcoverDimensions:288 pages, 9.21 × 6.14 × 0.75 inPublished:April 30, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198535988

ISBN - 13:9780198535980

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Table of Contents

Introduction1. Prime decomposition2. Kronecker Equivalence3. Arithmetical equivalence4. Arithmetical homomorphisms5. Kroneckerian fields6. Variations

Editorial Reviews

'...gives a very useful discussion of several 'generalisations and refinements of the theory developed in the preceding chapters, as well as [...] results from related areas which use the smae methods or lead to similar group theoretic problems' It may be regarded as a guide to the literature,and provides numerous sugggestions for further work' Bulletin London Mathematical Society