Galois groups associated with CM-fields, skew-symmetric matrices and orthogonal matrices

DOI10.1017/S0017089500009046zbMath0708.11055MaRDI QIDQ3490097

Stephen D. Cohen, R. W. K. Odoni

Publication date: 1990

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Galois groupcharacteristic polynomialsring of endomorphismsskew-symmetric matricesCM-fieldHilbert's irreducibility theoremsimple abelian varietycomplex-multiplicationdivision points on abelian varieties

Mathematics Subject Classification ID

Galois theory (11R32) Separable extensions, Galois theory (12F10) Other number fields (11R21) Complex multiplication and moduli of abelian varieties (11G15) Class field theory (11R37)

Related Items (2)

CM-fields and skew-symmetric matrices ⋮ Minimal dimension of symmetric or skew-symmetric matrices of given minimal polynomial

Cites Work

• Unnamed Item
• Eigenwerte und Minimalpolynome symmetrischer Matrizen in kommutativen Körpern
• The Galois groups of the polynomials \(X^ n+aX\ell +b\)
• The Galois group of a polynomial with two indeterminate coefficients
• The Galois groups of the polynomials \(x^ n+ax^ s+b\). II
• Characteristic polynomials of symmetric matrices
• The Galois Theory of Iterates and Composites of Polynomials
• Fields of definition of function fields and hurwitz families — groups as galois groups
• Galois Groups and Complex Multiplication

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