scholarly journals Unramified Subextensions of Ray Class Field Towers

2002 ◽  
Vol 249 (2) ◽  
pp. 528-543 ◽  
Author(s):  
Farshid Hajir ◽  
Christian Maire
Keyword(s):  
Class Field ◽  
Class Field Towers ◽  
Ray Class Field

scholarly journals Infinite class field towers

2009 ◽  
Vol 344 (4) ◽  
pp. 923-928 ◽  
Author(s):  
Jing Long Hoelscher
Keyword(s):  
Infinite Class ◽  
Class Field ◽  
Class Field Towers

scholarly journals Quadratic fields with infinite Hilbert 2-class field towers

2003 ◽  
Vol 106 (2) ◽  
pp. 151-158 ◽  
Author(s):  
Frank Gerth
Keyword(s):  
Quadratic Fields ◽  
Class Field ◽  
Class Field Towers

On Cyclic Fields of Odd Prime Degree p with Infinite Hilbert p-Class Field Towers

2002 ◽  
Vol 45 (1) ◽  
pp. 86-88 ◽  
Author(s):  
Frank Gerth
Keyword(s):  
Rational Numbers ◽  
Cyclic Extension ◽  
Prime Degree ◽  
Class Field ◽  
Positive Proportion ◽  
Class Field Towers ◽  
Class Field Tower

AbstractLet k be a cyclic extension of odd prime degree p of the field of rational numbers. If t denotes the number of primes that ramify in k, it is known that the Hilbert p-class field tower of k is infinite if t > 3 + 2 . For each t > 2 + , this paper shows that a positive proportion of such fields k have infinite Hilbert p-class field towers.

DISTRIBUTION OF GALOIS GROUPS OF MAXIMAL UNRAMIFIED 2-EXTENSIONS OVER IMAGINARY QUADRATIC FIELDS

2018 ◽  
Vol 237 ◽  
pp. 166-187
Author(s):  
SOSUKE SASAKI
Keyword(s):  
Class Group ◽  
Quadratic Field ◽  
Number Fields ◽  
Galois Groups ◽  
Quadratic Number ◽  
Imaginary Quadratic Fields ◽  
Class Field ◽  
Class Field Towers ◽  
Generalized Quaternion ◽  
Class Field Tower

Let $k$ be an imaginary quadratic field with $\operatorname{Cl}_{2}(k)\simeq V_{4}$. It is known that the length of the Hilbert $2$-class field tower is at least $2$. Gerth (On 2-class field towers for quadratic number fields with$2$-class group of type$(2,2)$, Glasgow Math. J. 40(1) (1998), 63–69) calculated the density of $k$ where the length of the tower is $1$; that is, the maximal unramified $2$-extension is a $V_{4}$-extension. In this paper, we shall extend this result for generalized quaternion, dihedral, and semidihedral extensions of small degrees.

scholarly journals On Class Field Towers and the Rank of Ideal Class Groups

1972 ◽  
Vol 48 ◽  
pp. 147-157 ◽  
Author(s):  
Yoshiomi Furuta
Keyword(s):  
Ideal Class ◽  
Class Groups ◽  
Infinite Class ◽  
Class Field ◽  
Ideal Class Groups ◽  
Class Field Towers

The following theorem on infinite class field towers is well-known.

Sign in / Sign up

Export Citation Format

Share Document