On ultrasolvable embedding problems with cyclic kernel

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

On 2-Groups as Galois Groups

1995 ◽  
Vol 47 (6) ◽  
pp. 1253-1273 ◽  
Author(s):  
Arne Ledet
Keyword(s):  
Galois Group ◽  
Direct Product ◽  
Galois Extension ◽  
Quaternion Algebra ◽  
Abelian Groups ◽  
Galois Groups ◽  
Embedding Problem ◽  
Brauer Group ◽  
Characteristic 2 ◽  
Cyclic Kernel

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.

The Universally Solvable Embedding Problem with Cyclic Kernel of Order 8

2004 ◽  
Vol 120 (4) ◽  
pp. 1603-1608
Author(s):  
V. V. Ishkhanov ◽  
B. B. Lur'e
Keyword(s):  
Embedding Problem ◽  
Universally Solvable ◽  
Cyclic Kernel

On the Ultrasolvability of p-Extensions of an Abelian Group by a Cyclic Kernel

2018 ◽  
Vol 232 (5) ◽  
pp. 662-676
Author(s):  
D. D. Kiselev
Keyword(s):  
Abelian Group ◽  
Cyclic Kernel

An Embedding Problem with Cyclic Kernel

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

scholarly journals The algebraic numbers definable in various exponential fields

2012 ◽  
Vol 11 (4) ◽  
pp. 825-834 ◽  
Author(s):  
Jonathan Kirby ◽  
Angus Macintyre ◽  
Alf Onshuus
Keyword(s):  
Algebraic Numbers ◽  
The Real ◽  
Cyclic Kernel

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.

On the Ultrasolvability of Some Classes of Minimal Nonsplit p-Extensions with Cyclic Kernel for p > 2

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

scholarly journals Resolution of a family of Galois embedding problems with cyclic kernel

2005 ◽  
pp. 111-132
Author(s):  
Montserrat Vela
Keyword(s):  
Cyclic Kernel

Metacyclic 2-Extensions with Cyclic Kernel and Ultrasolvability Questions

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

Embedding problems with cyclic kernel of order 4

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

Ultrasolvable and Sylow extensions with cyclic kernel

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