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Rigidity of Decomposition laws and number fields

Part of: Algebraic number theory: global fields Permutation groups

Published online by Cambridge University Press:  09 April 2009

Norbert Klingen
Norbert Klingen
Affiliation:
Mathematiches Institut Universität zu KölnWeyertal 86-90 D 5000 Köln 41, Germany
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Abstract

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We speak of rigidity, if partial information about the prime decomposition in an extension of number fields K¦k determines the decomposition law completely (and hence the zeta function ζK), or even fixes the field K itself. Several concepts of rigidity, depending on the degree of information we start from, are introduced and studied. The strongest concept (absolute rigidity) was only known to hold for the ground field and all quadratic extensions. Here a complete list of all Galois quartic extensions which are absolutely rigid is given. For the weaker concept of rigidity, all rigid situations among the fields of degree up to 8 are determined.

MSC classification

Secondary: 11R32: Galois theory 11R27: Units and factorization 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 2 , October 1991 , pp. 171 - 186
Copyright
Copyright © Australian Mathematical Society 1991

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