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

Acta Arithmetica (1995)

- Volume: 69, Issue: 2, page 153-169
- ISSN: 0065-1036

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topHourong Qin. "The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields." Acta Arithmetica 69.2 (1995): 153-169. <http://eudml.org/doc/206678>.

@article{HourongQin1995,

abstract = {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.},

author = {Hourong Qin},

journal = {Acta Arithmetica},

keywords = {tame kernel; imaginary quadratic field; Tate kernel; 4-rank},

language = {eng},

number = {2},

pages = {153-169},

title = {The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields},

url = {http://eudml.org/doc/206678},

volume = {69},

year = {1995},

}

TY - JOUR

AU - Hourong Qin

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

JO - Acta Arithmetica

PY - 1995

VL - 69

IS - 2

SP - 153

EP - 169

AB - 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.

LA - eng

KW - tame kernel; imaginary quadratic field; Tate kernel; 4-rank

UR - http://eudml.org/doc/206678

ER -

## References

top- [1] B. Brauckmann, The 2-Sylow subgroup of the tame kernel of number fields, Canad. J. Math. 43 (1991), 215-264. Zbl0729.11061
- [2] J. Browkin and A. Schinzel, On Sylow 2-subgroups of $K\u2082{O}_{F}$ for quadratic fields F, J. Reine Angew. Math. 331 (1982), 104-113.
- [3] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, London, 1978.
- [4] P. E. Conner and J. Hurrelbrink, Examples of quadratic number fields with K₂(O) containing no elements of order four, preprint. Zbl0844.11072
- [5] P. E. Conner and J. Hurrelbrink, The 4-rank of K₂(O), Canad. J. Math. 41 (1989), 932-960. Zbl0705.19006
- [6] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, New York, 1982. Zbl0482.10001
- [7] M. Kolster, The structure of the 2-Sylow subgroup of K₂(O), I , Comment. Math. Helv. 61 (1986), 576-588.
- [8] J. Milnor, Introduction to Algebraic K-theory, Ann. of Math. Stud. 72, Princeton University Press, 1971. Zbl0237.18005
- [9] J. Neukirch, Class Field Theory, Springer, Berlin, 1986. Zbl0587.12001
- [10] O. T. O'Meara, Introduction to Quadratic Forms, Springer, Berlin, 1963.
- [11] H. Qin, K₂ and algebraic number theory, Ph.D. Thesis, Nanjing University, 1992.
- [12] H. Qin, The 2-Sylow subgroups of $K\u2082{O}_{F}$ for real quadratic fields F, Science in China Ser. A 23 (12) (1993), 1254-1263.
- [13] J. Tate, Relations between K₂ and Galois cohomology, Invent. Math. 36 (1976), 257-274. Zbl0359.12011

## Citations in EuDML Documents

top- P. E. Conner, J. Hurrelbrink, On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
- Hourong Qin, The 4-rank of $K\u2082{O}_{F}$ for real quadratic fields F
- Marius Crainic, Paul Arne Østvær, On two-primary algebraic K-theory of quadratic number rings with focus on K₂

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