Displaying similar documents to “On metacyclic extensions”

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 .

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

Finite-dimensional differential algebraic groups and the Picard-Vessiot theory

Anand Pillay (2002)

Banach Center Publications

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We make some observations relating the theory of finite-dimensional differential algebraic groups (the ∂₀-groups of [2]) to the Galois theory of linear differential equations. Given a differential field (K,∂), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) ∂₀-groups G over K to Picard-Vessiot extensions L of K, such that G is K-split iff L = K. In fact we give a generalization to "K-good" ∂₀-groups. We also point out that the "Katz group" (a certain linear...