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1
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The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

100%
Qin H.
Acta Arithmetica
|
1995
|
tom 69
|
nr 2
153-169
EN
1. Introduction. Let F be a number field and $O_F$ the ring of its integers. Many results are known about the group $K₂O_F$, the tame kernel of F. In particular, many authors have investigated the 2-Sylow subgroup of $K₂O_F$. As compared with real quadratic fields, the 2-Sylow subgroups of $K₂O_F$ for imaginary quadratic fields F are more difficult to deal with. The objective of this paper is to prove a few theorems on the structure of the 2-Sylow subgroups of $K₂O_F$ for imaginary quadratic fields F. In our Ph.D. thesis (see [11]), we develop a method to determine the structure of the 2-Sylow subgroups of $K₂O_F$ for real quadratic fields F. The present paper is motivated by some ideas in the above thesis.
2
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The 4-rank of $K₂O_F$ for real quadratic fields F

100%
Qin H.
Acta Arithmetica
|
1995
|
tom 72
|
nr 4
323-333
EN
1. Introduction. Let F be a number field, and let $O_F$ be the ring of its integers. Several formulas for the 4-rank of $K₂O_F$ are known (see [7], [5], etc.). If √{-1) ∉ F, then such formulas are related to S-ideal class groups of F and F(√(-1)), and the numbers of dyadic places in F and F(√(-1)), where S is the set of infinite dyadic places of F. In [11], the author proposes a method which can be applied to determine the 4-rank of $K₂O_F$ for real quadratic fields F with 2 ∉ NF. The author also lists many real quadratic fields with the 2-Sylow subgroups of $K₂O_F$ being isomorphic to ℤ/2ℤ ⊕ ℤ/2ℤ ⊕ ℤ/4ℤ. In [12], the author gives a 4-rank $K₂O_F$ formula for imaginary quadratic fields F. By the formula, it is enough to compute some Legendre symbols when one wants to know 4-rank $K₂O_F$ for a given imaginary quadratic field F. In the present paper, we give a similar formula for real quadratic fields F. Then we give 4-rank $K₂O_F$ tables for real quadratic fields F = ℚ√d whose discriminants have at most three odd prime divisors.
3
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On the multiplicative independence of binomial coefficients

64%
Xia J., Qin H.
Acta Arithmetica
|
2005
|
tom 116
|
nr 3
289-292
4
Content available remote

The 8-rank of tame kernels of quadratic number fields

64%
Guo X., Qin H.
Acta Arithmetica
|
2012
|
tom 152
|
nr 4
407-424
5
Content available remote

The structure of the tame kernels of quadratic number fields (II)

51%
Yin X., Qin H., Zhu Q.
Acta Arithmetica
|
2005
|
tom 116
|
nr 3
217-262
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