The p -Dimension of Class Groups of Number Fields

1970 ◽  
Vol 2 (Part_3) ◽  
pp. 525-529 ◽  
Author(s):  
I. Connell ◽  
D. Sussman
Keyword(s):  
Number Fields ◽  
Class Groups

scholarly journals A Note on Ideal Class Groups

1966 ◽  
Vol 27 (1) ◽  
pp. 239-247 ◽  
Author(s):  
Kenkichi Iwasawa
Keyword(s):  
Class Group ◽  
Cyclotomic Field ◽  
Theoretical Method ◽  
Number Fields ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Class Groups ◽  
Algebraic Number Fields ◽  
Ideal Class Groups ◽  
The Ideal

In the first part of the present paper, we shall make some simple observations on the ideal class groups of algebraic number fields, following the group-theoretical method of Tschebotarew. The applications on cyclotomic fields (Theorems 5, 6) may be of some interest. In the last section, we shall give a proof to a theorem of Kummer on the ideal class group of a cyclotomic field.

scholarly journals Correction to: Stickelberger ideals and Fitting ideals of class groups for abelian number fields

2019 ◽  
Vol 374 (3-4) ◽  
pp. 2083-2088
Author(s):  
Masato Kurihara ◽  
Takashi Miura
Keyword(s):  
Number Fields ◽  
Class Groups

scholarly journals On class groups of random number fields

2020 ◽  
Vol 121 (4) ◽  
pp. 927-953
Author(s):  
Alex Bartel ◽  
Hendrik W. Lenstra
Keyword(s):  
Random Number ◽  
Number Fields ◽  
Class Groups

Capitulation in the cyclotomic ℤ2 extension of CM number fields

2018 ◽  
Vol 166 (2) ◽  
pp. 371-380
Author(s):  
KATHARINA MÜLLER
Keyword(s):  
Number Field ◽  
Number Fields ◽  
Class Groups ◽  
Definition Of

AbstractLet 𝕂n be the intermediate steps in the cyclotomic ℤp-extension of a CM number field 𝕂. For p ⧧ 2 the minus part of the p-class groups is given by An− = $\frac{1}{2}$(1 − j)An. We will give a new definition of the minus part for p = 2 and will prove that there is no finite submodule in lim∞←nAn−. Furthermore we will show that μ = 0 if and only if μ− = 0 in this new definition.

scholarly journals On the 16-Rank of Class Groups of ℚ(√-2p) for Primes p ≡ 1 mod 4

2018 ◽  
Vol 2019 (23) ◽  
pp. 7406-7427 ◽  
Author(s):  
Peter Koymans ◽  
Djordjo Milovic
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Class Groups ◽  
Quadratic Number Fields

Abstract We use Vinogradov’s method to prove equidistribution of a spin symbol governing the 16-rank of class groups of quadratic number fields $\mathbb{Q}(\sqrt{-2p})$, where p ≡ 1 mod 4 is a prime.

scholarly journals Bounds on $2$-torsion in class groups of number fields and integral points on elliptic curves

2020 ◽  
Vol 33 (4) ◽  
pp. 1087-1099 ◽  
Author(s):  
M. Bhargava ◽  
A. Shankar ◽  
T. Taniguchi ◽  
F. Thorne ◽  
J. Tsimerman ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Number Fields ◽  
Class Groups ◽  
Integral Points
Sign in / Sign up

Export Citation Format

Share Document