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

• Autorzy: Hourong Qin
• Języki publikacji: EN

Abstrakty

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 2
• Strony: 153-169

Daty

wydano

1995

otrzymano

1993-09-03

poprawiono

1994-01-18

Twórcy

autor

Hourong Qin

• Department of Mathematics, Nanjing University, Nanjing, 210008, P.R. China

Bibliografia

• [1] B. Brauckmann, The 2-Sylow subgroup of the tame kernel of number fields, Canad. J. Math. 43 (1991), 215-264.
• [2] J. Browkin and A. Schinzel, On Sylow 2-subgroups of $K₂O_F$ 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.
• [5] P. E. Conner and J. Hurrelbrink, The 4-rank of K₂(O), Canad. J. Math. 41 (1989), 932-960.
• [6] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, New York, 1982.
• [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.
• [9] J. Neukirch, Class Field Theory, Springer, Berlin, 1986.
• [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 $K₂O_F$ 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.