On equivalent number fields with special Galois groups
type: Item
instance of: scholarly article
title: On equivalent number fields with special Galois groups
zbMATH Open document ID: 0789.12003
DOI: 10.1007/BF02761692
author: Manfred Lochter
published in: Israel Journal of Mathematics
publication date: 1994-01-16T00:00:00Z
review text: The word equivalent in the title means Sonn-equivalence introduced by \textit{J. Sonn} [Isr. J. Math. 52, 239-244 (1985; Zbl 0592.12006)], where it was shown that two equivalent number fields have equal normal closures. It is proved that equivalent fields of degree \(\leq 5\) over \(\mathbb{Q}\) are conjugate. An analogous result is shown to be true if the Galois group of the common normal closure is the full symmetric group. Furthermore, relations between Sonn-, Kronecker- and arithmetical equivalence are discussed. \{Reviewer's remark: A wealth of further material can be found in the author's dissertation (Köln 1992; Zbl 0776.11064)\}.
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12F05
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 474985
zbMATH Keywords: Kronecker-equivalence
zbMATH Keywords: Sonn-equivalence
zbMATH Keywords: equivalent fields
zbMATH Keywords: arithmetical equivalence
reviewed by: Rolf Brandl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 474985