On Quadratic Number Fields Each Having an Unramified Extension Which Properly Contains the Hilbert Class Field of its Genus Field

2004 ◽  
pp. 271-286 ◽  
Author(s):  
Ken Yamamura
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Class Field ◽  
Quadratic Number Fields ◽  
Genus Field ◽  
Hilbert Class Field

scholarly journals Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields: Corrigenda

1994 ◽  
Vol 50 (2) ◽  
pp. 351-352
Author(s):  
Elliot Benjamin
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Class Field ◽  
Quadratic Number Fields ◽  
Imaginary Quadratic Number ◽  
Hilbert Class Field

In my earlier paper [1] I made the claim that there are three groups in Hall and Senior's book “The Groups of Order 2n(n ≤ 6)” that are in error (groups 64/140, 64/141, 64/143). However, it has been pointed out to me by Franz Lemermeyer that I made the unfortunate oversight of using the definition [x, y] = xyx−1y−1 for the commutator whereas Hall and Senion use the definition [x, y] = x−1y−1xy (see [2]). With this correction there is no problem with the above three groups in Hall and Senior.

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