class field towers
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2020 ◽  
Vol 373 ◽  
pp. 107318
Author(s):  
Farshid Hajir ◽  
Christian Maire ◽  
Ravi Ramakrishna

2020 ◽  
Vol 44 (4) ◽  
pp. 1466-1483 ◽  
Author(s):  
Mohamed Mahmoud CHEMS-EDDIN ◽  
Abdelkader ZEKHNINI ◽  
Abdelmalek AZIZI

2019 ◽  
Vol 158 (1) ◽  
pp. 103-118
Author(s):  
Abdelmalek Azizi ◽  
Idriss Jerrari ◽  
Abdelkader Zekhnini ◽  
Mohammed Talbi

2018 ◽  
Vol 237 ◽  
pp. 166-187
Author(s):  
SOSUKE SASAKI

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.


2015 ◽  
Vol 147 ◽  
pp. 766-777 ◽  
Author(s):  
Michael R. Bush ◽  
Daniel C. Mayer

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