On the inverse problem of Galois theory. Núria Vila (1992) Publicacions Matemàtiques Similarity: 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 Hopf Galois structures and complete groups. Childs, Lindsay N. (2003) The New York Journal of Mathematics [electronic only] Similarity:
Galois groups of fields of definition of solvable branched coverings Sybilla Beckmann (1988) Compositio Mathematica Similarity:
On double covers of the generalized alternating group ℤ d ≀ m as Galois groups over algebraic number fields Martin Epkenhans (1997) Acta Arithmetica Similarity: 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 .
Galois embedding of algebraic variety and its application to abelian surface Hisao Yoshihara (2007) Rendiconti del Seminario Matematico della Università di Padova Similarity:
Solvable-by-finite groups as differential Galois groups Claude Mitschi, Michael F. Singer (2002) Annales de la Faculté des sciences de Toulouse : Mathématiques Similarity:
Invariants and differential Galois groups in degree four Julia Hartmann (2002) Banach Center Publications Similarity: This note extends the algorithm of [hess] for computing unimodular Galois groups of irreducible differential equations of order four. The main tool is invariant theory.
Recent work on differential Galois theory Marius Van der Put (1997-1998) Séminaire Bourbaki Similarity:
On the product formula in Galois groups. Kay Wingberg (1986) Journal für die reine und angewandte Mathematik Similarity: