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The Sylow p-Subgroups of Tame Kernels in Dihedral Extensions of Number Fields

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let F/E be a Galois extension of number fields with Galois group D2n. In this paper, we give some expressions for the order of the Sylow p-subgroups of tame kernels of F and some of its subfields containing E, where p is an odd prime. As applications, we give some results about the order of the Sylow p-subgroups when F/E is a Galois extension of number fields with Galois group D16.
Rocznik
Strony
113--121
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
  • School of Mathematical Sciences Nanjing Normal University Nanjing, 210023 P.R. China
autor
  • School of Mathematical Sciences Nanjing Normal University Nanjing, 210023 P.R. China
Bibliografia
  • [1] J. Browkin, On the p-rank of the tame kernel of algebraic number fields, J. Reine Angew. Math. 432 (1992), 135-149.
  • [2] J. Browkin, Tame kernels of cubic cyclic fields, Math. Comp. 74 (2005), 967-999.
  • [3] J. Browkin, Tame and wild kernels of quadratic imaginary number fields, Math. Comp. 68 (1999), 291-305.
  • [4] J. Browkin and H. Gangl, Tame kernels and second regulators of number fields and their sub fields, submitted to the volume dedicated to Professor Aderemi O. KuKu.
  • [5] F. Keune, On the structure of K2 of the ring of integers in a number field, K-Theory 2 (1989), 625-645.
  • [6] H. R. Qin, The 2-Sylow subgroup of K2(OF ) for number fields F, J. Algebra 284 b(2005), 494-519.
  • [7] H. R. Qin, The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields, Acta Arith. 69 (1995), 153-169.
  • [8] H. R. Qin, The 4-rank of K2(OF ) for real quadratic fields, Acta Arith. 72 (1995), 323-333.
  • [9] D. Quillen, Finite generation of the groups Ki of rings of algebraic integers, in: Lecture Notes in Math. 341, Springer, 1973, 179-198.
  • [10] C. Soul_e, Groupes de Chow et K-théorie de variétés sur un corps fini, Math. Ann. 268 (1984), 317-345.
  • [11] J. Tate, Relation between K2 and Galois cohomology, Invent. Math. 36 (1976), 257-274.
  • [12] H. Y. Zhou, Odd parts of tame kernels of dihedral extensions, Acta Arith. 156 (2012), 341-349.
  • [13] H. Y. Zhou, The tame kernel of multiquadratic number fields, Comm. Algebra 37 (2009), 630-638.
  • [14] H. Y. Zhou, Tame kernels of cubic cyclic fields, Acta Arith. 124 (2006), 293-313.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a3a7a976-0546-4155-a8d5-aabe9a2e519b
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