On ultrasolvable embedding problems with cyclic kernel

2016 ◽  
Vol 71 (6) ◽  
pp. 1149-1151 ◽  
Author(s):  
D D Kiselev
Keyword(s):  

1995 ◽  
Vol 47 (6) ◽  
pp. 1253-1273 ◽  
Author(s):  
Arne Ledet

AbstractLet L/K be a finite Galois extension in characteristic ≠ 2, and consider a non-split Galois theoretical embedding problem over L/K with cyclic kernel of order 2. In this paper, we prove that if the Galois group of L/K is the direct product of two subgroups, the obstruction to solving the embedding problem can be expressed as the product of the obstructions to related embedding problems over the corresponding subextensions of L/K and certain quaternion algebra factors in the Brauer group of K. In connection with this, the obstructions to realising non-abelian groups of order 8 and 16 as Galois groups over fields of characteristic ≠ 2 are calculated, and these obstructions are used to consider automatic realisations between groups of order 4, 8 and 16.



2004 ◽  
Vol 120 (4) ◽  
pp. 1603-1608
Author(s):  
V. V. Ishkhanov ◽  
B. B. Lur'e




2005 ◽  
Vol 130 (3) ◽  
pp. 4724-4728
Author(s):  
V. V. Ishkhanov ◽  
B. B. Lur’e


2012 ◽  
Vol 11 (4) ◽  
pp. 825-834 ◽  
Author(s):  
Jonathan Kirby ◽  
Angus Macintyre ◽  
Alf Onshuus

AbstractWe prove the following theorems. Theorem 1: for any E-field with cyclic kernel, in particular ℂ or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: for the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers.



2018 ◽  
Vol 232 (5) ◽  
pp. 677-692
Author(s):  
D. D. Kiselev ◽  
I. A. Chubarov
Keyword(s):  




2019 ◽  
Vol 240 (4) ◽  
pp. 447-458
Author(s):  
D. D. Kiselev
Keyword(s):  


1998 ◽  
Vol 106 (1) ◽  
pp. 109-131 ◽  
Author(s):  
Arne Ledet
Keyword(s):  


2018 ◽  
Vol 30 (1) ◽  
pp. 95-102
Author(s):  
D. D. Kiselev ◽  
A. V. Yakovlev
Keyword(s):  


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