Displaying similar documents to “On the Galois cohomology group of the ring of integers in an algebraic number field”

Lifting solutions over Galois rings.

Javier Gómez-Calderón (1990)

Extracta Mathematicae

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In this note we generalize some results from finite fields to Galois rings which are finite extensions of the ring Zm of integers modulo p where p is a prime and m ≥ 1.

On the inverse problem of Galois theory.

Núria Vila (1992)

Publicacions Matemàtiques

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The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.

On double covers of the generalized alternating group ℤ d ≀ m as Galois groups over algebraic number fields

Martin Epkenhans (1997)

Acta Arithmetica

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Let ℤ d ≀ m b e t h e g e n e r a l i z e d a l t e r n a t i n g g r o u p . W e p r o v e t h a t a l l d o u b l e c o v e r s o f ℤd ≀ m o c c u r a s G a l o i s g r o u p s o v e r a n y a l g e b r a i c n u m b e r f i e l d . W e f u r t h e r r e a l i z e s o m e o f t h e s e d o u b l e c o v e r s a s t h e G a l o i s g r o u p s o f r e g u l a r e x t e n s i o n s o f ℚ ( T ) . I f d i s o d d a n d m > 7 , t h e n e v e r y c e n t r a l e x t e n s i o n o f ℤd ≀ m o c c u r s a s t h e G a l o i s g r o u p o f a r e g u l a r e x t e n s i o n o f ℚ ( T ) . W e f u r t h e r i m p r o v e s o m e o f o u r e a r l i e r r e s u l t s c o n c e r n i n g d o u b l e c o v e r s o f t h e g e n e r a l i z e d s y m m e t r i c g r o u p ℤd ≀ m .

On Galois structure of the integers in cyclic extensions of local number fields

G. Griffith Elder (2002)

Journal de théorie des nombres de Bordeaux

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Let p be a rational prime, K be a finite extension of the field of p -adic numbers, and let L / K be a totally ramified cyclic extension of degree p n . Restrict the first ramification number of L / K to about half of its possible values, b 1 > 1 / 2 · p e 0 / ( p - 1 ) where e 0 denotes the absolute ramification index of K . Under this loose condition, we explicitly determine the ℤ p [ G ] -module structure of the ring of integers of L , where ℤ p denotes the p -adic integers and G denotes the Galois group Gal ( L / K ) . In the process of determining...

Local Class Field Theory via Lubin-Tate Theory

Teruyoshi Yoshida (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].