PSL$(2,7)$ septimic fields with a power basis

Melisa J. Lavallee; Blair K. Spearman; Qiduan Yang

Displaying similar documents to “PSL $(2, 7)$ septimic fields with a power basis”

Nonsolvable nonic number fields ramified only at one small prime

Sylla Lesseni (2006)

Journal de Théorie des Nombres de Bordeaux

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We prove that there is no primitive nonic number field ramified only at one small prime. So there is no nonic number field ramified only at one small prime and with a nonsolvable Galois group.

PAC fields over number fields

Moshe Jarden (2006)

Journal de Théorie des Nombres de Bordeaux

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We prove that if $K$ is a number field and $N$ is a Galois extension of $ℚ$ which is not algebraically closed, then $N$ is not PAC over $K$ .

A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic $p$

Nigel P. Byott (2011)

Journal de Théorie des Nombres de Bordeaux

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Let $S / R$ be a finite extension of discrete valuation rings of characteristic $p > 0$ , and suppose that the corresponding extension $L / K$ of fields of fractions is separable and is $H$ -Galois for some $K$ -Hopf algebra $H$ . Let $𝔻_{S / R}$ be the different of $S / R$ . We show that if $S / R$ is totally ramified and its degree $n$ is a power of $p$ , then any element $ρ$ of $L$ with $v_{L} (ρ) \equiv - v_{L} (𝔻_{S / R}) - 1 (mod n)$ generates $L$ as an $H$ -module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. G. Elder for Galois...

The class number one problem for the dihedral and dicyclic CM-fields

Stéphane Louboutin (1999)

Colloquium Mathematicae

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We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.

On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.

Chipchakov, Ivan D. (2005)

Acta Universitatis Apulensis. Mathematics - Informatics

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Displaying similar documents to “PSL ( 2 , 7 ) septimic fields with a power basis”

Nonsolvable nonic number fields ramified only at one small prime

PAC fields over number fields

A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic p

The class number one problem for the dihedral and dicyclic CM-fields

On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.

Displaying similar documents to “PSL $(2, 7)$ septimic fields with a power basis”

A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic $p$