Displaying similar documents to “C4-Extensions of Sn as Galois Groups.”

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.

Groups of Order 32 as Galois Groups

Michailov, Ivo (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12F12. We find the obstructions to realizability of groups of order 32 as Galois groups over arbitrary field of characteristic not 2. We discuss explicit extensions and automatic realizations as well. This work is partially supported by project of Shumen University

On realizability of p-groups as Galois groups

Michailov, Ivo M., Ziapkov, Nikola P. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12F12, 15A66. In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related...

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 .